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arXiv · 1711.09045

On a non-periodic modified Euler equation: existence and quasi-invariant measures

Ana Bela Cruzeiro·Alexandra Symeonides
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Abstract

We consider a modified Euler equation on $\mathbb R^2$. We prove existence of weak global solutions for bounded (and fast decreasing at infinity) initial conditions and construct Gibbs-type measures on function spaces which are quasi-invariant for the Euler flow. Almost everywhere with respect to such measures (and, in particular, for less regular initial conditions), the flow is shown to be also globally defined.

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Ana Bela Cruzeiro, Alexandra Symeonides. 2017-11-24. On a non-periodic modified Euler equation: existence and quasi-invariant measures. https://arxiv.org/abs/1711.09045

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