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

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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

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

Received March 2005 Revised November 2005 Published April 2006

Abstract
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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 & Continuous Dynamical Systems - B, 2006, 6 (4) : 697-709. doi: 10.3934/dcdsb.2006.6.697

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