Invariant measures for stochastic damped 2D Euler equations

Hakima Bessaih; Benedetta Ferrario

doi:10.1007/s00220-020-03714-3

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arXiv · 1909.00424

Invariant measures for stochastic damped 2D Euler equations

Hakima Bessaih·Benedetta Ferrario

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Abstract

We study the two-dimensional Euler equations, damped by a linear term and driven by an additive noise. The existence of weak solutions has already been studied; pathwise uniqueness is known for solutions that have vorticity in $L^\infty$. In this paper, we prove the Markov property and then the existence of an invariant measure in the space $L^\infty$ by means of a Krylov-Bogoliubov's type method, working with the weak$\star$ and the bounded weak$\star$ topologies in $L^\infty$.

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BibTeX RIS

Hakima Bessaih, Benedetta Ferrario. 2019-09-01. Invariant measures for stochastic damped 2D Euler equations. https://doi.org/10.1007/s00220-020-03714-3

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