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arXiv · 2009.02049

Growth of perimeter for vortex patches in a bulk

Kyudong Choi·In-Jee Jeong
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Abstract

We consider the two-dimensional incompressible Euler equations. We construct vortex patches with smooth boundary on $T^2$ and $R^2$ whose perimeter grows with time. More precisely, for any constant $M > 0$, we construct a vortex patch in $T^2$ whose smooth boundary has length of order 1 at the initial time such that the perimeter grows up to the given constant $M$ within finite time. The construction is done by cutting a thin stick out of an almost square patch. A similar result holds for an almost round patch with a thin handle in $R^2$.

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Kyudong Choi, In-Jee Jeong. 2020-09-04. Growth of perimeter for vortex patches in a bulk. https://arxiv.org/abs/2009.02049

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