Stationary solutions for stochastic damped Navier-Stokes equations in\n mathbb R^d

2017/02/02 by Zdzisław Brzeźniak, Brzeźniak, Zdzisław, Benedetta Ferrario +1
Economics, Econometrics and Finance · Engineering · Mathematics · #60H15 #76D06 #76M35 #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1702.00697

openalex publication_date 2017/02/02 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

We consider the stochastic damped Navier-Stokes equations in mathbb R^d\n(d=2,3), assuming as in our previous work [4] that the covariance of the\nnoise is not too regular, so It ^o calculus cannot be applied in the space of\nfinite energy vector fields. We prove the existence of an invariant measure\nwhen d=2 and of a stationary solution when d=3.\n

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