Jump To The First Citation Point In The Article1
Andersson, L., ``The global existence problem in general relativity'', (November, 1999), [Online Los Alamos Archive Preprint]: cited on 4 December 1999, External Linkhttp://xxx.lanl.gov/abs/gr-qc/9911032 .
Jump To The First Citation Point In The Article2
Andersson, L., Chrusciel, P. T., and Friedrich, H., ``On the regularity of solutions to the Yamabe equation and the existence of smooth hyperboloidal initial data for Einstein's field equations'', Commun. Math. Phys., 149, 587-612, (1992).
Jump To The First Citation Point In The Article3
Andréasson, H., ``Regularity of the gain term and strong tex2html_wrap_inline1869 convergence to equilibrium for the relativistic Boltzmann equation'', SIAM J. Math. Anal., 27, 1386-1405, (1996).
Jump To The First Citation Point In The Article4
Andréasson, H., ``Global foliations of matter spacetimes with Gowdy symmetry'', Commun. Math. Phys., 206, 337-365, (1999).
Jump To The First Citation Point In The Article5
Anguige, K., ``Isotropic cosmological singularities 3: The Cauchy problem for the inhomogeneous conformal Einstein-Vlasov equations'', (March, 1999), [Online Los Alamos Archive Preprint]: cited on 21 September 1999, External Linkhttp://xxx.lanl.gov/abs/gr-qc/9903018 .
Jump To The First Citation Point In The Article6
Anguige, K., ``A class of plane symmetric perfect-fluid cosmologies with a Kasner-like singularity'', (August, 1999), [Online Los Alamos Archive Preprint]: cited on 21 September 1999, External Linkhttp://xxx.lanl.gov/abs/gr-qc/9908072 .
Jump To The First Citation Point In The Article7
Anguige, K., and Tod, K. P., ``Isotropic cosmological singularities 1: Polytropic perfect fluid spacetimes'', Ann. Phys. (N. Y.), 276, 257-293, (1999).
Jump To The First Citation Point In The Article8
Anguige, K., and Tod, K. P., ``Isotropic cosmological singularities 2: The Einstein-Vlasov system'', Ann. Phys. (N. Y.), 276, 294-320, (1999).
Jump To The First Citation Point In The Article9
Arkeryd, L., ``On the strong tex2html_wrap_inline1869 trend to equilibrium for the Boltzmann equation'', Stud. Appl. Math., 87, 283-288, (1992).
Jump To The First Citation Point In The Article10
Arnold, V. I., and Ilyashenko, Yu. S., ``Ordinary differential equations'', in Anosov, D.V., and Arnold, V.I., eds., Dynamical Systems I., 1-148, (Springer, Berlin, 1988).
Jump To The First Citation Point In The Article11
Aubin, T., Nonlinear Analysis on Manifolds. Monge-Ampère equations, (Springer, Berlin, 1982).
Jump To The First Citation Point In The Article12
Baouendi, M. S., and Goulaouic, C., ``Remarks on the abstract form of nonlinear Cauchy-Kovalevsky theorems'', Commun. Part. Diff. Eq., 2, 1151-1162, (1977).
Jump To The First Citation Point In The Article13
Bartnik, R., ``Remarks on cosmological spacetimes and constant mean curvature hypersurfaces'', Commun. Math. Phys., 117, 615-624, (1988).
Jump To The First Citation Point In The Article14
Bartnik, R., ``Quasi-spherical metrics and prescribed scalar curvature'', J. Differ. Geom., 37, 31-71, (1993).
Jump To The First Citation Point In The Article15
Bartnik, R., and Fodor, G., ``On the restricted validity of the thin sandwich conjecture'', Phys. Rev. D, 48, 3596-3599, (1993).
Jump To The First Citation Point In The Article16
Bartnik, R., and McKinnon, J., ``Particlelike solutions of the Einstein-Yang-Mills equations'', Phys. Rev. Lett., 61, 141-143, (1988).
Jump To The First Citation Point In The Article17
Batt, J., Faltenbacher, W., and Horst, E., ``Stationary spherically symmetric models in stellar dynamics'', Arch. Rat. Mech. Anal., 93, 159-183, (1986).
Jump To The First Citation Point In The Article18
Beale, J. T., Hou, T. Y., and Lowengrub, J. S., ``Growth rates for the linearized motion of fluid interfaces away from equilibrium'', Commun. Pure Appl. Math., 46, 1269-1301, (1993).
Jump To The First Citation Point In The Article19
Belinskii, V. A., Khalatnikov, I. M., and Lifshitz, E. M., ``Oscillatory approach to a singular point in the relativistic cosmology'', Adv. Phys., 19, 525-573, (1970).
Jump To The First Citation Point In The Article20
Belinskii, V. A., Khalatnikov, I. M., and Lifshitz, E. M., ``A general solution of the Einstein equations with a time singularity'', Adv. Phys., 31, 639-667, (1982).
Jump To The First Citation Point In The Article21
Berger, B. K., Chrusciel, P. T., Isenberg, J., and Moncrief, V., ``Global foliations of vacuum spacetimes with tex2html_wrap_inline1873 isometry'', Ann. Phys. (N. Y.), 260, 117-148, (1997).
Jump To The First Citation Point In The Article22
Berger, B. K., Chrusciel, P. T., and Moncrief, V., ``On asymptotically flat spacetimes with tex2html_wrap_inline1875 -invariant Cauchy surfaces'', Ann. Phys. (N. Y.), 237, 322-354, (1995).
Jump To The First Citation Point In The Article23
Beyer, H., ``The spectrum of adiabatic stellar oscillations'', J. Math. Phys., 36, 4792-4814, (1995).
Jump To The First Citation Point In The Article24
Binney, J., and Tremaine, S., Galactic dynamics, (Princeton University Press, Princeton, 1987).
Jump To The First Citation Point In The Article25
Bourguignon, J.-P., ``Stabilité par déformation non-linéaire de la métrique de Minkowski (d'après D. Christodoulou et S. Klainerman)'', Astérisque, 201-203, 321-358, (1992).
Jump To The First Citation Point In The Article26
Brauer, U., ``Singularitäten in relativistischen Materiemodellen'', Thesis, University of Potsdam, (1995).
Jump To The First Citation Point In The Article27
Brauer, U., Rendall, A. D., and Reula, O. A., ``The cosmic no-hair theorem and the nonlinear stability of homogeneous Newtonian cosmological models'', Class. Quantum Grav., 11, 2283-2296, (1994).
Jump To The First Citation Point In The Article28
Bressan, A., ``The unique limit of the Glimm scheme'', Arch. Rat. Mech. Anal., 130, 205-230, (1995).
Jump To The First Citation Point In The Article29
Bressan, A., and Colombo, R. M., ``The semigroup generated by tex2html_wrap_inline1877 conservation laws'', Arch. Rat. Mech. Anal., 133, 1-75, (1995).
Jump To The First Citation Point In The Article30
Brodbeck, O., Heusler, M., Straumann, N., and Volkov, M., ``Rotating solitons and non-rotating non-static black holes'', Phys. Rev. Lett., 79, 4310-4313, (1997).
Jump To The First Citation Point In The Article31
Burnett, G. A., and Rendall, A. D., ``Existence of maximal hypersurfaces in some spherically symmetric spacetimes'', Class. Quantum Grav., 13, 111-123, (1996).
Jump To The First Citation Point In The Article32
Cantor, M., ``A necessary and sufficient condition for York data to specify an asymptotically flat spacetime'', J. Math. Phys., 20, 1741-1744, (1979).
Jump To The First Citation Point In The Article33
Cercignani, C., The Boltzmann equation and its applications, (Springer, Berlin, 1994).
Jump To The First Citation Point In The Article34
Cercignani, C., Illner, R., and Pulvirenti, M., The mathematical theory of dilute gases, (Springer, Berlin, 1988).
Jump To The First Citation Point In The Article35
Chemin, J.-Y., ``Remarques sur l'apparition de singularités dans les écoulements Euleriens compressibles'', Commun. Math. Phys., 133, 323-339, (1990).
Jump To The First Citation Point In The Article36
Chen, J., ``Conservation laws for the relativistic p -system'', Commun. Part. Diff. Eq., 20, 1605-1646, (1995).
Jump To The First Citation Point In The Article37
Chen, J., ``Conservation laws for relativistic fluid dynamics'', Arch. Rat. Mech. Anal., 139, 377-398, (1997).
Jump To The First Citation Point In The Article38
Choptuik, M. W., ``Universality and scaling in the gravitational collapse of a scalar field'', Phys. Rev. Lett., 70, 9-12, (1993).
Jump To The First Citation Point In The Article39
Choquet-Bruhat, Y., and Geroch, R., ``Global aspects of the Cauchy problem in general relativity'', Commun. Math. Phys., 14, 329-335, (1969).
Jump To The First Citation Point In The Article40
Choquet-Bruhat, Y., Isenberg, J., and York, J. W., ``Einstein constraints on asymptotically Euclidean manifolds'', (June, 1999), [Online Los Alamos Archive Preprint]: cited on 20 August 1999, External Linkhttp://xxx.lanl.gov/abs/gr-qc/9906095 .
Jump To The First Citation Point In The Article41
Choquet-Bruhat, Y., and York, J., ``The Cauchy problem'', in Held, A., ed., General relativity and gravitation, volume 1, 99-172, (Plenum, New York, 1980).
Jump To The First Citation Point In The Article42
Christodoulou, D., ``Global existence of generalised solutions of the spherically symmetric Einstein-scalar equations in the large'', Commun. Math. Phys., 106, 587-621, (1986).
Jump To The First Citation Point In The Article43
Christodoulou, D., ``The problem of a self-gravitating scalar field'', Commun. Math. Phys., 105, 337-361, (1986).
Jump To The First Citation Point In The Article44
Christodoulou, D., ``A mathematical theory of gravitational collapse'', Commun. Math. Phys., 109, 613-647, (1987).
Jump To The First Citation Point In The Article45
Christodoulou, D., ``The structure and uniqueness of generalised solutions of the spherically symmetric Einstein-scalar equations'', Commun. Math. Phys., 109, 591-611, (1987).
Jump To The First Citation Point In The Article46
Christodoulou, D., ``The formation of black holes and singularities in spherically symmetric gravitational collapse'', Commun. Pure Appl. Math., 44, 339-373, (1991).
Jump To The First Citation Point In The Article47
Christodoulou, D., ``Bounded variation solutions of the spherically symmetric Einstein-scalar field equations'', Commun. Pure Appl. Math., 46, 1131-1220, (1993).
Jump To The First Citation Point In The Article48
Christodoulou, D., ``Examples of naked singularity formation in the gravitational collapse of a scalar field'', Ann. Math., 140, 607-653, (1994).
Jump To The First Citation Point In The Article49
Christodoulou, D., ``Self-gravitating fluids: a two-phase model'', Arch. Rat. Mech. Anal., 130, 343-400, (1995).
Jump To The First Citation Point In The Article50
Christodoulou, D., ``Self-gravitating fluids: the continuation and termination of a free phase boundary'', Arch. Rat. Mech. Anal., 133, 333-398, (1996).
Jump To The First Citation Point In The Article51
Christodoulou, D., ``Self-gravitating fluids: the formation of a free phase boundary in the phase transition from soft to hard'', Arch. Rat. Mech. Anal., 134, 97-154, (1996).
Jump To The First Citation Point In The Article52
Christodoulou, D., ``The instability of naked singularities in the gravitational collapse of a scalar field'', Ann. Math., 149, 183-217, (1999).
Jump To The First Citation Point In The Article53
Christodoulou, D., and Klainerman, S., ``Asymptotic properties of linear field equations in Minkowski space'', Commun. Pure Appl. Math., 43, 137-199, (1990).
Jump To The First Citation Point In The Article54
Christodoulou, D., and Klainerman, S., The global nonlinear stability of the Minkowski space, (Princeton University Press, Princeton, 1993).
Jump To The First Citation Point In The Article55
Christodoulou, D., and Ó Murchadha, N., ``The boost problem in general relativity'', Commun. Math. Phys., 10, 271-300, (1981).
Jump To The First Citation Point In The Article56
Christodoulou, D., and Tahvildar-Zadeh, A. S., ``On the asymptotic behaviour of spherically symmetric wave maps'', Duke Math. J., 71, 31-69, (1993).
Jump To The First Citation Point In The Article57
Christodoulou, D., and Tahvildar-Zadeh, A. S., ``On the regularity of spherically symmetric wave maps'', Commun. Pure Appl. Math., 46, 1041-1091, (1993).
Jump To The First Citation Point In The Article58
Chrusciel, P. T., ``On spacetimes with tex2html_wrap_inline1384 symmetric compact Cauchy surfaces'', Ann. Phys. (N. Y.), 202, 100-150, (1990).
Jump To The First Citation Point In The Article59
Chrusciel, P. T., On the uniqueness in the large of solutions of Einstein's equations. (Strong cosmic censorship.), volume 20 of Proc. Centre Math. Anal., (Australian National University, Canberra, 1991).
Jump To The First Citation Point In The Article60
Chrusciel, P. T., ``Semi-global existence and convergence of solutions of the Robinson-Trautman (2-dimensional Calabi) equation'', Commun. Math. Phys., 137, 289-313, (1991).
Jump To The First Citation Point In The Article61
Chrusciel, P. T., Isenberg, J., and Moncrief, V., ``Strong cosmic censorship in polarised Gowdy spacetimes'', Class. Quantum Grav., 7, 1671-1680, (1990).
Jump To The First Citation Point In The Article62
Claudel, C. M., and Newman, K. P., ``The Cauchy problem for quasi-linear hyperbolic evolution problems with a singularity in the time'', Proc. R. Soc. London, Ser. A, 454, 1073-1107, (1998).
Jump To The First Citation Point In The Article63
DiPerna, R. J., and Lions, P.-L., ``On the Cauchy problem for Boltzmann equations: global existence and weak stability'', Ann. Math., 130, 321-366, (1989).
Jump To The First Citation Point In The Article64
Dossa, M., ``Espaces de Sobolev non isotropes, à poids et problèmes de Cauchy quasi-linéaires sur un conoïde caractéristique'', Ann. Inst. Henri Poincaré, A., 66, 37-107, (1997).
Jump To The First Citation Point In The Article65
Dudynski, M., and Ekiel-Jezewska, M., ``Global existence proof for the relativistic Boltzmann equation'', J. Stat. Phys., 66, 991-1001, (1992).
Jump To The First Citation Point In The Article66
Eardley, D., and Moncrief, V., ``The global existence of Yang-Mills fields in tex2html_wrap_inline1883 '', Commun. Math. Phys., 83, 171-212, (1982).
Jump To The First Citation Point In The Article67
Ehlers, J., ``The Newtonian limit of general relativity'', in Ferrarese, G., ed., Classical mechanics and relativity: relationship and consistency, (Bibliopolis, Naples, 1991).
Jump To The First Citation Point In The Article68
Evans, L. C., Partial differential equations, (American Mathematical Society, Providence, 1998).
Jump To The First Citation Point In The Article69
Friedrich, H., ``Existence and structure of past asymptotically simple solutions of Einstein's field equations with positive cosmological constant'', J. Geom. Phys., 3, 101-117, (1986).
Jump To The First Citation Point In The Article70
Friedrich, H., ``On the global existence and asymptotic behaviour of solutions to the Einstein-Yang-Mills equations'', J. Differ. Geom., 34, 275-345, (1991).
Jump To The First Citation Point In The Article71
Friedrich, H., ``Einstein equations and conformal structure: Existence of anti-de Sitter-type spacetimes'', J. Geom. Phys., 17, 125-184, (1995).
Jump To The First Citation Point In The Article72
Friedrich, H., ``Hyperbolic reductions of Einstein's field equations'', Class. Quantum Grav., 13, 1451-1469, (1996).
Jump To The First Citation Point In The Article73
Friedrich, H., ``Evolution equations for gravitating ideal fluid bodies in general relativity'', Phys. Rev. D, 57, 2317-2322, (1998).
Jump To The First Citation Point In The Article74
Friedrich, H., ``Gravitational fields near spacelike and null infinity'', J. Geom. Phys., 24, 83-172, (1998).
Jump To The First Citation Point In The Article75
Friedrich, H., and Nagy, G., ``The initial boundary value problem for Einstein's vacuum field equations'', Commun. Math. Phys., 201, 619-655, (1999).
Jump To The First Citation Point In The Article76
Fritelli, S., and Reula, O., ``On the Newtonian limit of general relativity'', Commun. Math. Phys., 166, 221-235, (1994).
Jump To The First Citation Point In The Article77
Glassey, R. T., and Schaeffer, J., ``The `two and one half dimensional' relativistic Vlasov-Maxwell system'', Commun. Math. Phys., 185, 257-284, (1997).
Jump To The First Citation Point In The Article78
Glassey, R. T., and Schaeffer, J., ``The relativistic Vlasov-Maxwell system in two space dimensions. Part 1'', Arch. Rat. Mech. Anal., 141, 331-354, (1998).
Jump To The First Citation Point In The Article79
Glassey, R. T., and Schaeffer, J., ``The relativistic Vlasov-Maxwell system in two space dimensions. Part 2'', Arch. Rat. Mech. Anal., 141, 355-374, (1998).
Jump To The First Citation Point In The Article80
Glassey, R. T., and Strauss, W., ``Asymptotic stability of the relativistic Maxwellian'', Publ. Math. RIMS Kyoto, 29, 167-233, (1993).
Jump To The First Citation Point In The Article81
Glimm, J., ``Solutions in the large for nonlinear hyperbolic systems of equations'', Commun. Pure Appl. Math., 18, 697-715, (1965).
Jump To The First Citation Point In The Article82
Goliath, M., Nilsson, U., and Uggla, C., ``Spatially self-similar spherically symmetric perfect-fluid models'', Class. Quantum Grav., 15, 167-186, (1998).
Jump To The First Citation Point In The Article83
Goliath, M., Nilsson, U., and Uggla, C., ``Timelike self-similar spherically symmetric perfect-fluid models'', Class. Quantum Grav., 15, 2841-2863, (1998).
Jump To The First Citation Point In The Article84
Grassin, M., ``Global smooth solutions to Euler equations for a perfect gas'', Indiana Univ. Math. J., 47, 1397-1432, (1998).
Jump To The First Citation Point In The Article85
Gundlach, C., ``Critical Phenomena in Gravitational Collapse'', (December, 1999), [Living Reviews in Relativity]: cited on 22 December 1999, http://www.livingreviews.org/Articles/Volume2/1999-4gundlach .
Jump To The First Citation Point In The Article86
Gundlach, C., ``Critical phenomena in gravitational collapse'', Adv. Theor. Math. Phys., 2, 1-49, (1998).
Jump To The First Citation Point In The Article87
Guo, Y., ``Smooth irrotational flows in the large to the Euler-Poisson system'', Commun. Math. Phys., 195, 249-265, (1998).
Jump To The First Citation Point In The Article88
Guo, Y., and Rein, G., ``Stable steady states in stellar dynamics'', to appear in Arch. Rat. Mech. Anal.
Jump To The First Citation Point In The Article89
Guo, Y., and Tahvildar-Zadeh, A. S., ``Formation of singularities in relativistic fluid dynamics and in spherically symmetric plasma dynamics'', in Chen, G.-Q., and DiBenedetto, E., eds., Nonlinear partial differential equations, (AMS, Providence, 1999).
Jump To The First Citation Point In The Article90
Hartman, P., Ordinary Differential Equations, (Birkhäuser, Basel, 1982).
Jump To The First Citation Point In The Article91
Hauser, I., and Ernst, F. J., ``Group structure of the solution manifold of the hyperbolic Ernst equation - general study of the subject and detailed elaboration of mathematical proofs'', (March, 1999), [Online Los Alamos Archive Preprint]: cited on 4 December 1999, External Linkhttp://xxx.lanl.gov/abs/gr-qc/9903104 .
Jump To The First Citation Point In The Article92
Heilig, U., ``On the existence of rotating stars in general relativity'', Commun. Math. Phys., 166, 457-493, (1995).
Jump To The First Citation Point In The Article93
Heusler, M., ``Stationary black holes: uniqueness and beyond'', (May, 1998), [Living Reviews in Relativity]: cited on 12 December 1999, http://www.livingreviews.org/Articles/Volume1/1998-6heusler .
Jump To The First Citation Point In The Article94
Heusler, M., Black hole uniqueness theorems, (Cambridge University Press, Cambridge, 1996).
Jump To The First Citation Point In The Article95
Hubbard, J. H., and West, B. H., Differential equations: a dynamical systems approach., (Springer, Berlin, 1991).
Jump To The First Citation Point In The Article96
Isenberg, J., ``Constant mean curvature solutions of the Einstein constraint equations on closed manifolds'', Class. Quantum Grav., 12, 2249-2274, (1995).
Jump To The First Citation Point In The Article97
Isenberg, J., and Kichenassamy, S., ``Asymptotic behaviour in polarized tex2html_wrap_inline1873 -symmetric vacuum spacetimes'', J. Math. Phys., 40, 340-352, (1999).
Jump To The First Citation Point In The Article98
Isenberg, J., and Moncrief, V., ``Asymptotic behaviour of the gravitational field and the nature of singularities in Gowdy spacetimes'', Ann. Phys. (N. Y.), 199, 84-122, (1990).
Jump To The First Citation Point In The Article99
Isenberg, J., and Moncrief, V., ``A set of nonconstant mean curvature solutions of the Einstein constraint equations on closed manifolds'', Class. Quantum Grav., 13, 1819-1847, (1996).
Jump To The First Citation Point In The Article100
Isenberg, J., and Rendall, A. D., ``Cosmological spacetimes not covered by a constant mean curvature slicing'', Class. Quantum Grav., 15, 3679-3688, (1998).
Jump To The First Citation Point In The Article101
John, F., Partial differential equations, (Springer, Berlin, 1982).
Jump To The First Citation Point In The Article102
John, F., Nonlinear wave equations, formation of singularities, (American Mathematical Society, Providence, 1990).
Jump To The First Citation Point In The Article103
Kichenassamy, S., ``The blow-up problem for exponential nonlinearities'', Commun. Part. Diff. Eq., 21, 125-162, (1996).
Jump To The First Citation Point In The Article104
Kichenassamy, S., ``Fuchsian equations in Sobolev spaces and blow-up'', J. Differ. Equations, 125, 299-327, (1996).
Jump To The First Citation Point In The Article105
Kichenassamy, S., Nonlinear wave equations, (Marcel Dekker, New York, 1996).
Jump To The First Citation Point In The Article106
Kichenassamy, S., and Littman, W., ``Blow-up surfaces for nonlinear wave equations, I'', Commun. Part. Diff. Eq., 18, 431-452, (1993).
Jump To The First Citation Point In The Article107
Kichenassamy, S., and Littman, W., ``Blow-up surfaces for nonlinear wave equations, II'', Commun. Part. Diff. Eq., 18, 1869-1899, (1993).
Jump To The First Citation Point In The Article108
Kichenassamy, S., and Rendall, A. D., ``Analytic description of singularities in Gowdy spacetimes'', Class. Quantum Grav., 15, 1339-1355, (1998).
Jump To The First Citation Point In The Article109
Kind, S., and Ehlers, J., ``Initial boundary value problem for the spherically symmetric Einstein equations for a perfect fluid'', Class. Quantum Grav., 18, 2123-2136, (1993).
Jump To The First Citation Point In The Article110
Klainerman, S., and Machedon, M., ``Finite energy solutions of the Yang-Mills equations in tex2html_wrap_inline1887 '', Ann. Math., 142, 39-119, (1995).
Jump To The First Citation Point In The Article111
Klainerman, S., and Nicoló, F., ``On local and global aspects of the Cauchy problem in general relativity'', Class. Quantum Grav., 16, R73-R157, (1999).
Jump To The First Citation Point In The Article112
Kleihaus, B., and Kunz, J., ``Static axially symmetric Einstein-Yang-Mills-dilaton solutions: I. Regular solutions'', Phys. Rev. D, 57, 834-856, (1998).
Jump To The First Citation Point In The Article113
Lifshitz, E. M., and Khalatnikov, I. M., ``Investigations in relativistic cosmology'', Adv. Phys., 12, 185-249, (1963).
Jump To The First Citation Point In The Article114
Lin, S. S., ``Stability of gaseous stars in spherically symmetric motions'', SIAM J. Math. Anal., 28, 539-569, (1997).
Jump To The First Citation Point In The Article115
Lindblom, L., and Masood-ul Alam, A. K. M., ``On the spherical symmetry of static stellar models'', Commun. Math. Phys., 162, 123-145, (1994).
Jump To The First Citation Point In The Article116
Lions, P.-L., ``Compactness in Boltzmann's equation via Fourier integral operators and applications'', J. Math. Kyoto Univ., 34, 391-427, (1994).
Jump To The First Citation Point In The Article117
Lions, P.-L., and Perthame, B., ``Propagation of moments and regularity for the three-dimensional Vlasov-Poisson system'', Invent. Math., 105, 415-430, (1991).
Jump To The First Citation Point In The Article118
Majda, A., Compressible fluid flow and systems of conservation laws in several space dimensions., (Springer, Berlin, 1984).
Jump To The First Citation Point In The Article119
Makino, T., ``On spherically symmetric stellar models in general relativity'', J. Math. Kyoto Univ., 38, 55-69, (1998).
Jump To The First Citation Point In The Article120
Moncrief, V., ``Global properties of Gowdy spacetimes with tex2html_wrap_inline1889 topology'', Ann. Phys. (N. Y.), 132, 87-107, (1981).
Jump To The First Citation Point In The Article121
Moncrief, V., ``Neighbourhoods of Cauchy horizons in cosmological spacetimes with one Killing field'', Ann. Phys. (N. Y.), 141, 83-103, (1982).
Jump To The First Citation Point In The Article122
Moncrief, V., and Eardley, D., ``The global existence problem and cosmic censorship in general relativity'', Gen. Relativ. Gravit., 13, 887-892, (1981).
Jump To The First Citation Point In The Article123
Mucha, P. B., ``Global existence for the Einstein-Boltzmann equation in flat Robertson-Walker spacetime'', Commun. Math. Phys., 203, 107-118, (1999).
Jump To The First Citation Point In The Article124
Newman, R. P. A. C., ``On the structure of conformal singularities in classical general relativity'', Proc. R. Soc. London, 443, A473-492; A493-515, (1993).
Jump To The First Citation Point In The Article125
Park, J., ``Static solutions of the Einstein equations for spherically symmetric elastic bodies'', (October, 1998), [Online Los Alamos Archive Preprint]: cited on 17 August 1999, External Linkhttp://xxx.lanl.gov/abs/gr-qc/9810010 .
Jump To The First Citation Point In The Article126
Pfaffelmoser, K., ``Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data'', J. Differ. Equations, 95, 281-303, (1992).
Jump To The First Citation Point In The Article127
Racke, R., Lectures on nonlinear evolution problems, (Vieweg, Wiesbaden, 1992).
Jump To The First Citation Point In The Article128
Rein, G., ``Stationary and static stellar dynamical models with axial symmetry.'', to appear in Journal of Nonlinear Analysis.
Jump To The First Citation Point In The Article129
Rein, G., ``Generic global solutions of the relativistic Vlasov-Maxwell system of plasma physics'', Commun. Math. Phys., 135, 41-78, (1990).
Jump To The First Citation Point In The Article130
Rein, G., ``Static solutions of the spherically symmetric Vlasov-Einstein system'', Math. Proc. Cambridge, 115, 559-570, (1994).
Jump To The First Citation Point In The Article131
Rein, G., ``Cosmological solutions of the Vlasov-Einstein system with spherical, plane and hyperbolic symmetry'', Math. Proc. Cambridge, 119, 739-762, (1996).
Jump To The First Citation Point In The Article132
Rein, G., ``Nonlinear stability of homogeneous models in Newtonian cosmology'', Arch. Rat. Mech. Anal., 140, 335-351, (1997).
Jump To The First Citation Point In The Article133
Rein, G., and Rendall, A. D., ``Compact support of spherically symmetric equilibria in relativistic and non-relativistic galactic dynamics'', (December, 1998), [Online Los Alamos Archive Preprint]: cited on 17 August 1999, External Linkhttp://xxx.lanl.gov/abs/gr-qc/9812061 .
Jump To The First Citation Point In The Article134
Rein, G., and Rendall, A. D., ``Global existence of solutions of the spherically symmetric Vlasov-Einstein system with small initial data'', Commun. Math. Phys., 150, 561-583, (1992).
Jump To The First Citation Point In The Article135
Rein, G., and Rendall, A. D., ``Smooth static solutions of the spherically symmetric Vlasov-Einstein system'', Ann. Inst. Henri Poincarè, A., 59, 383-397, (1993).
Jump To The First Citation Point In The Article136
Rein, G., and Rendall, A. D., ``Global existence of classical solutions to the Vlasov-Poisson system in a three dimensional, cosmological setting'', Arch. Rat. Mech. Anal., 126, 183-201, (1994).
Jump To The First Citation Point In The Article137
Rein, G., Rendall, A. D., and Schaeffer, J., ``A regularity theorem for solutions of the spherically symmetric Vlasov-Einstein system'', Commun. Math. Phys., 168, 467-478, (1995).
Jump To The First Citation Point In The Article138
Rein, G., Rendall, A. D., and Schaeffer, J., ``Critical collapse of collisionless matter - a numerical investigation'', Phys. Rev. D, 58, 044007, (1998).
Jump To The First Citation Point In The Article139
Rendall, A. D., ``Reduction of the characteristic initial value problem to the Cauchy problem and its applications to the Einstein equations'', Proc. R. Soc. London, Ser. A, 427, 221-239, (1990).
Jump To The First Citation Point In The Article140
Rendall, A. D., ``The initial value problem for a class of general relativistic fluid bodies'', J. Math. Phys., 33, 1047-1053, (1992).
Jump To The First Citation Point In The Article141
Rendall, A. D., ``On the definition of post-Newtonian approximations'', Proc. R. Soc. London, Ser. A, 438, 341-360, (1992).
Jump To The First Citation Point In The Article142
Rendall, A. D., ``The Newtonian limit for asymptotically flat solutions of the Vlasov-Einstein system'', Commun. Math. Phys., 163, 89-112, (1994).
Jump To The First Citation Point In The Article143
Rendall, A. D., ``Crushing singularities in spacetimes with spherical, plane and hyperbolic symmetry'', Class. Quantum Grav., 12, 1517-1533, (1995).
Jump To The First Citation Point In The Article144
Rendall, A. D., ``Constant mean curvature foliations in cosmological spacetimes'', Helv. Phys. Acta, 69, 490-500, (1996).
Jump To The First Citation Point In The Article145
Rendall, A. D., ``Existence and non-existence results for global constant mean curvature foliations'', Nonlinear Anal., 30, 3589-3598, (1997).
Jump To The First Citation Point In The Article146
Rendall, A. D., ``Existence of constant mean curvature hypersurfaces in spacetimes with two-dimensional local symmetry'', Commun. Math. Phys., 189, 145-164, (1997).
Jump To The First Citation Point In The Article147
Rendall, A. D., ``Global dynamics of the mixmaster model'', Class. Quantum Grav., 14, 2341-2356, (1997).
Jump To The First Citation Point In The Article148
Rendall, A. D., ``An introduction to the Einstein-Vlasov system'', Banach Center Publ., 41, 35-68, (1997).
Jump To The First Citation Point In The Article149
Rendall, A. D., ``Solutions of the Einstein equations with matter'', in Francaviglia, M., Longhi, G., Lusanna, L., and Sorace, E., eds., Proceedings of the 14th International Conference on General Relativity and Gravitation, 313-335, (World Scientific, Singapore, 1997).
Jump To The First Citation Point In The Article150
Rendall, A. D., and Schmidt, B. G., ``Existence and properties of spherically symmetric static fluid bodies with given equation of state'', Class. Quantum Grav., 8, 985-1000, (1991).
Jump To The First Citation Point In The Article151
Rendall, A. D., and Tod, K. P., ``Dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations which are locally rotationally symmetric'', Class. Quantum Grav., 16, 1705-1726, (1999).
Jump To The First Citation Point In The Article152
Ringström, H., ``Curvature blow up in Bianchi VIII and IX vacuum spacetimes'', (November, 1999), [Online Los Alamos Archive Preprint]: cited on 4 December 1999, External Linkhttp://xxx.lanl.gov/abs/gr-qc/9911115 .
Jump To The First Citation Point In The Article153
Schaeffer, J., ``A class of counterexamples to Jeans' theorem for the Vlasov-Einstein system'', Commun. Math. Phys., 204, 313-327, (1999).
Jump To The First Citation Point In The Article154
Secchi, P., ``On the equations of viscous gaseous stars'', Ann. Scuola Norm. Sup. Pisa, 18, 295-318, (1991).
Jump To The First Citation Point In The Article155
Shapiro, S. L., and Teukolsky, S. A., ``Relativistic stellar dynamics on the computer. II Physical applications'', Astrophys. J., 298, 58-79, (1985).
Jump To The First Citation Point In The Article156
Sideris, T., ``Formation of singularities in three-dimensional compressible fluids'', Commun. Math. Phys., 101, 475-485, (1979).
Jump To The First Citation Point In The Article157
Smoller, J., and Temple, B., ``Global solutions of the relativistic Euler equations'', Commun. Math. Phys., 156, 65-100, (1993).
Jump To The First Citation Point In The Article158
Smoller, J. A., Wasserman, A. G., Yau, S. T., and Mcleod, J. B., ``Smooth static solutions of the Einstein-Yang-Mills equations'', Commun. Math. Phys., 143, 115-147, (1991).
Jump To The First Citation Point In The Article159
Strauss, W., Nonlinear wave equations, (American Mathematical Society, Providence, 1989).
Jump To The First Citation Point In The Article160
Taylor, M. E., Pseudodifferential operators and nonlinear PDE, (Birkhäuser, Boston, 1991).
Jump To The First Citation Point In The Article161
Taylor, M. E., Partial differential equations, (Springer, Berlin, 1996).
Jump To The First Citation Point In The Article162
Tod, K. P., ``Isotropic singularities'', Rend. Sem. Mat. Univ. Politec. Torino, 50, 69-93, (1992).
Jump To The First Citation Point In The Article163
Wainwright, J., and Ellis, G. F. R., Dynamical Systems in Cosmology, (Cambridge University Press, Cambridge, 1997).
Jump To The First Citation Point In The Article164
Wainwright, J. A., Hancock, M. J., and Uggla, C., ``Asymptotic self-similarity breaking at late times in cosmology'', Class. Quantum Grav., 16, 2577-2598, (1999).
Jump To The First Citation Point In The Article165
Weaver, M., ``Dynamics of magnetic Bianchi VI tex2html_wrap_inline1891 cosmologies.'', (September, 1999), [Online Los Alamos Archive Preprint]: cited on 21 September 1999, External Linkhttp://xxx.lanl.gov/abs/gr-qc/9909043 .
Jump To The First Citation Point In The Article166
Witt, D., ``Vacuum spacetimes that admit no maximal slice'', Phys. Rev. Lett., 57, 1386-1389, (1986).
Jump To The First Citation Point In The Article167
Woodhouse, N. M. J., ``Integrability and Einstein's equations'', Banach Center Publ., 41, 221-232, (1997).
Jump To The First Citation Point In The Article168
Wu, S., ``Well-posedness in Sobolev spaces of the full water wave problem in 3-D'', J. Amer. Math. Soc., 12, 445-495, (1999).
Jump To The First Citation Point In The Article169
York, J. W., ``Conformal `thin-sandwich' data for the initial value problem of general relativity'', Phys. Rev. Lett., 82, 1350-1353, (1999).
image Local and Global Existence Theorems for the Einstein Equations
Alan D. Rendall
http://www.livingreviews.org/lrr-2000-1
© Max-Planck-Gesellschaft. ISSN 1433-8351
Problems/Comments to livrev@aei-potsdam.mpg.de