### 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 |

State | Published - Jul 2006 |

### Fingerprint

### 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

**Lyapunov exponents for stochastic differential equations with infinite memory and application to stochastic Navier-stokes equations.** / Bakhtin, Yuri.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Lyapunov exponents for stochastic differential equations with infinite memory and application to stochastic Navier-stokes equations

AU - Bakhtin, Yuri

PY - 2006/7

Y1 - 2006/7

N2 - 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.

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.

KW - Linear cocycle

KW - Lyapunov exponents

KW - Multiplicative ergodic theorem

KW - Navier-Stokes system

KW - Stochastic delay equation

UR - http://www.scopus.com/inward/record.url?scp=33745310753&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33745310753&partnerID=8YFLogxK

M3 - Article

VL - 6

SP - 697

EP - 709

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

SN - 1531-3492

IS - 4

ER -