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July  2006, 6(4): 697-709. doi: 10.3934/dcdsb.2006.6.697

Lyapunov exponents for stochastic differential equations with infinite memory and application to stochastic Navier-Stokes equations

Yuri Bakhtin 1,

1. 

Mathematics Department, Duke University, Box 90320, Durham, NC 27708-0320, United States

Received  March 2005 Revised  November 2005 Published  April 2006

We prove an Oseledets-type theorem for differential equations with a right-hand side that depends on the history of the solution via a random linear operator. This result is applied then to a linear system with memory obtained from the linearized Stochastic Navier--Stokes system on the 2D torus.
Keywords: linear cocycle, Lyapunov exponents, Navier-Stokes system., multiplicative ergodic theorem, Stochastic delay equation.
Mathematics Subject Classification: Primary: 34K50; Secondary: 37H15, 60H1.
Citation: Yuri Bakhtin. Lyapunov exponents for stochastic differential equations with infinite memory and application to stochastic Navier-Stokes equations. Discrete and Continuous Dynamical Systems - B, 2006, 6 (4) : 697-709. doi: 10.3934/dcdsb.2006.6.697
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