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

Yuri Bakhtin

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

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	697-709
Number of pages	13
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	6
Issue number	4
DOIs	https://doi.org/10.3934/dcdsb.2006.6.697
State	Published - Jul 2006

Keywords

Linear cocycle
Lyapunov exponents
Multiplicative ergodic theorem
Navier-Stokes system
Stochastic delay equation

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcdsb.2006.6.697

Cite this

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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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AB - 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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KW - Multiplicative ergodic theorem

KW - Navier-Stokes system

KW - Stochastic delay equation

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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