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Large Deviation Principle and Inviscid Shell Models

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1.	Title	Title of document	Large Deviation Principle and Inviscid Shell Models
2.	Creator	Author's name, affiliation, country	Hakima Bessaih; University of Wyoming; United States
2.	Creator	Author's name, affiliation, country	Annie Millet; University Paris 1; France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Shell models of turbulence; viscosity coefficient and inviscid models; stochastic PDEs; large deviations
3.	Subject	Subject classification	60H15 ; 60F10 ; 76D06 ; 76M35
4.	Description	Abstract	LDP is proved for the inviscid shell model of turbulence. As the viscosity coefficient converges to 0 and the noise intensity is multiplied by its square root, we prove that some shell models of turbulence with a multiplicative stochastic perturbation driven by a $H$-valued Brownian motion satisfy a LDP in $\mathcal{C}([0,T],V)$ for the topology of uniform convergence on $[0,T]$, but where $V$ is endowed with a topology weaker than the natural one. The initial condition has to belong to $V$ and the proof is based on the weak convergence of a family of stochastic control equations. The rate function is described in terms of the solution to the inviscid equation.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	This work was partially written while H. Bessaih was invited professor at the University of Paris 1. The work of this author has also been supported by the NSF grant No. DMS 0608494.
7.	Date	(YYYY-MM-DD)	2009-11-26
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/719
10.	Identifier	Digital Object Identifier	10.1214/EJP.v14-719
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 14
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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