Uniqueness of solutions of the stochastic Navier-Stokes equation with invariant measure given by the enstrophy

Abstract

A stochastic Navier-Stokes equation with space-time Gaussian white noise is considered, having as infinitesimal invariant measure a Gaussian measure μ_ν whose covariance is given in terms of the enstrophy. Pathwise uniqueness for μ_ν-a.e. initial velocity is proven for solutions having μ_ν as invariant measure.

Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/009117904000000379

Cited by in corpus (18)

• A theory of regularity structures
• Invariant Gibbs measures of the energy for shell models of turbulence; the inviscid and viscous cases
• Convergence of stochastic 2D inviscid Boussinesq equations with transport noise to a deterministic viscous system
• Hyperviscous stochastic Navier-Stokes equations with white noise invariant measure in two dimensions
• Stochastic mSQG equations with multiplicative transport noises: white noise solutions and scaling limit
• $L^1$-Uniqueness of Kolmogorov Operators Associated to 2D Stochastic Navier-Stokes Coriolis Equations with Space-Time White Noise
• Convergence of transport noise to Ornstein-Uhlenbeck for 2D Euler equations under the enstrophy measure
• Scaling limit of stochastic 2D Euler equations with transport noises to the deterministic Navier-Stokes equations
• Gaussian invariant measures and stationary solutions of 2D Primitive Equations
• On the infinite dimension limit of invariant measures and solutions of Zeitlin's 2D Euler equations
• Point vortex approximation for 2D Navier--Stokes equations driven by space-time white noise
• Fokker-Planck equations for SPDE with non-trace class noise
• Scaling Limits for Stochastic SQG Equations and 2D Inviscid Critical Boussinesq Equations with Transport Noises
• Existence and Uniqueness of Energy Solutions to the Stochastic Diffusive Surface Quasi-Geostrophic Equation with Additive Noise
• 2D hydrodynamical systems: invariant measures of Gaussian type
• On Stochastic Shell Models of Turbulence
• 2D Navier-Stokes equation in Besov spaces of negative order
• 2D Navier-Stokes equation with cylindrical fractional Brownian noise