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arXiv · 1310.6128

Exponential growth of the vorticity gradient for the Euler equation on the torus

Andrej Zlatos
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Abstract

We prove that there are solutions to the Euler equation on the torus with $C^{1,α}$ vorticity and smooth except at one point such that the vorticity gradient grows in $L^\infty$ at least exponentially as $t\to\infty$. The same result is shown to hold for the vorticity Hessian and smooth solutions. Our proofs use a version of a recent result by Kiselev and Sverak.

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Andrej Zlatos. 2014-10-08. Exponential growth of the vorticity gradient for the Euler equation on the torus. https://arxiv.org/abs/1310.6128

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