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Surface Stretching for Ornstein Uhlenbeck Velocity Fields


 
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1. Title Title of document Surface Stretching for Ornstein Uhlenbeck Velocity Fields
 
2. Creator Author's name, affiliation, country Rene Carmona; Princeton University
 
2. Creator Author's name, affiliation, country Stanislav Grishin; Princeton University
 
2. Creator Author's name, affiliation, country Lin Xu; Princeton University
 
2. Creator Author's name, affiliation, country Stanislav Molchanov; University of North Carolina at Charlotte
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) Diffusion Processes, Lyapunov Exponent, Stochastic Flows.
 
3. Subject Subject classification 60H10, 60H30
 
4. Description Abstract The present note deals with large time properties of the Lagrangian trajectories of a turbulent flow in $R^2$ and $R^3$. We assume that the flow is driven by an incompressible time-dependent random velocity field with Gaussian statistics. We also assume that the field is homogeneous in space and stationary and Markovian in time. Such velocity fields can be viewed as (possibly infinite dimensional) Ornstein-Uhlenbeck processes. In d spatial dimensions we established the (strict) positivity of the sum of the largest $d-1$ Lyapunov exponents. As a consequences of this result, we prove the exponential stretching of surface areas (when $d=3$) and of curve lengths (when $d=2$.) This confirms conjectures found in the theory of turbulent flows.
 
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7. Date (YYYY-MM-DD) 1996-01-25
 
8. Type Status & genre Peer-reviewed Article
 
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9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/980
 
10. Identifier Digital Object Identifier 10.1214/ECP.v2-980
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 2
 
12. Language English=en en
 
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