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arXiv · 1612.08587

Invariant measures for the non-periodic two-dimensional Euler equation

Ana Bela Cruzeiro·Alexandra Symeonides
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Abstract

We construct Gaussian invariant measures for the two-dimensional Euler equation on the plane. We show the existence of solution with initial conditions in the support of the measures, namely $H^\beta_{loc}(\R^2)$ with $\beta<-1$. Uniqueness and continuity of the velocity flow are proved.

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Ana Bela Cruzeiro, Alexandra Symeonides. 2016-12-27. Invariant measures for the non-periodic two-dimensional Euler equation. https://arxiv.org/abs/1612.08587

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