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

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)697-709
Number of pages13
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume6
Issue number4
StatePublished - Jul 2006

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Stochastic Navier-Stokes Equation
Random Operators
Navier-Stokes System
Stochastic Systems
Lyapunov Exponent
Navier Stokes equations
Linear Operator
Stochastic Equations
Linear systems
Torus
Differential equations
Linear Systems
Differential equation
Data storage equipment
Theorem
History

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Cite this

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title = "Lyapunov exponents for stochastic differential equations with infinite memory and application to stochastic Navier-stokes equations",
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.",
keywords = "Linear cocycle, Lyapunov exponents, Multiplicative ergodic theorem, Navier-Stokes system, Stochastic delay equation",
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KW - Multiplicative ergodic theorem

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KW - Stochastic delay equation

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