Stationary solutions of nonlinear stochastic evolution equations1

DOI10.1080/07362999708809502zbMath0899.60056OpenAlexW2097541073MaRDI QIDQ4371837

Pao-Liu Chow, Rafail Z. Khasminskii

Publication date: 12 November 1998

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/07362999708809502

zbMATH Keywords

Navier-Stokes equationsinvariant measuresrandom perturbationsexistence and uniquenessparabolic Itô equations

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items (24)

Layer methods for stochastic Navier-Stokes equations using simplest characteristics ⋮ On stochastic evolution equations for nonlinear bipolar fluids: well-posedness and some properties of the solution ⋮ On the behavior of solutions to certain parabolic SPDE's driven by Wiener processes. ⋮ Delay differential equations driven by Lévy processes: stationarity and Feller properties ⋮ Well-posedness and asymptotic behavior of stochastic convective Brinkman-Forchheimer equations perturbed by pure jump noise ⋮ A Note on the Solution of a Stochastic Partial Differential Equation ⋮ On the stochastic 2-D motion of a Bingham fluid ⋮ Some rigorous results on a stochastic GOY model ⋮ Well posedness, large deviations and ergodicity of the stochastic 2D Oldroyd model of order one ⋮ Large deviation principle for occupation measures of stochastic generalized Burgers-Huxley equation ⋮ Stochastic control of tidal dynamics equation with Lévy noise ⋮ Dynamics and Large Deviations for Fractional Stochastic Partial Differential Equations with Lévy Noise ⋮ Local times for solutions of the complex Ginzburg-Landau equation and the inviscid limit ⋮ Infinite-dimensional Hamilton-Jacobi-Bellman equations in gauss-sobolev spaces ⋮ Rigorous remarks about scaling laws in turbulent fluids ⋮ Markov selections for the 3D stochastic Navier-Stokes equations ⋮ Existence and uniqueness of stationary solutions for 3D Navier-Stokes system with small random forcing via stochastic cascades ⋮ Lyapunov Functions and Stationary Distributions of Stochastic Evolution Equations ⋮ Irreducibility and exponential mixing of some stochastic hydrodynamical systems driven by pure jump noise ⋮ Asymptotics of solutions to semilinear stochastic wave equations ⋮ Deterministic and stochastic equations of motion arising in Oldroyd fluids of order one: existence, uniqueness, exponential stability and invariant measures ⋮ Ergodicity of Stochastic Shell Models Driven by Pure Jump Noise ⋮ Impulse control of stochastic Navier-Stokes equations ⋮ Invariant measure and random attractors for stochastic differential equations with delay

Cites Work

• Global flows with invariant (Gibbs) measures for Euler and Navier-Stokes two dimensional fluids
• Exit problem and control theory
• Parabolic Ito equations with monotone nonlinearities
• Stochastic partial differential equations in Hölder spaces
• Strong Feller property and irreducibility for diffusions on Hilbert spaces
• Equations stochastiques du type Navier-Stokes
• Stochastic partial differential equations and filtering of diffusion processes
• Mathematical Problems of Statistical Hydromechanics
• Uniqueness and stability of invariant measures for stochastic differential equations in hilbert spaces
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Stationary solutions of nonlinear stochastic evolution equations¹