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NUMBER M20083
AUTHOR Jeong, In-Jee
TITLE Growth of perimeter for vortex patches in a bulk
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JOURNAL APPLIED MATHEMATICS LETTERS, 2021
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 slit out of an almost square patch. A similar result holds for an almost round patch with a thin handle in R-2. (c) 2020 Elsevier Ltd. All rights reserved.
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