Lyapunov exponents for stochastic differential equations withinfinite memory and application to stochastic Navier-Stokesequations

Yuri Bakhtin

doi:10.3934/dcdsb.2006.6.697

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2006, Volume 6, Issue 4: 697-709. Doi: 10.3934/dcdsb.2006.6.697

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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

Received: February 28, 2005

Revised: October 31, 2005

Published: June 2006

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Abstract

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.

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Mathematics Subject Classification: Primary: 34K50; Secondary: 37H15, 60H15.

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

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