Random attractors for stochastic 2D-Navier-Stokes equations in some unbounded domains

2011/03/20 by Brzeźniak, Z., Caraballo, T., Langa, J. A. +3 · 2 citations
#35B41 #35Q35 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1103.3889

Abstract

We show that the stochastic flow generated by the Stochastic Navier-Stokes equations in a 2-dimensional Poincaré domain has a unique random attractor. This result complements a recent result by Brzeźniak and Li [10] who showed that the flow is asymptotically compact and generalizes a recent result by Caraballo et al. [12] who proved existence of a unique pullback attractor for the time-dependent deterministic Navier-Stokes equations in a 2-dimensional Poincaré domain.

Cited by

• (H,H²)-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus
• Random dynamics and invariant measures for a class of non-Newtonian fluids of differential type on 2D and 3D Poincaré domains

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