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

Zdzisław Brzeźniak; Benedetta Ferrario

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arXiv · 1702.00697

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

Zdzisław Brzeźniak·Benedetta Ferrario

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Abstract

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

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Zdzisław Brzeźniak, Benedetta Ferrario. 2017-02-02. Stationary solutions for stochastic damped Navier-Stokes equations in $\mathbb R^d$. https://arxiv.org/abs/1702.00697

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