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arXiv · 2108.01811

Infinite growth in vorticity gradient of compactly supported planar vorticity near Lamb dipole

Kyudong Choi·In-Jee Jeong
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Abstract

We prove linear in time filamentation for perturbations of the Lamb dipole, which is a traveling wave solution to the incompressible Euler equations in $\mathbb{R}^2$. The main ingredient is a recent nonlinear orbital stability result by Abe-Choi. As a consequence, we obtain linear in time growth for the vorticity gradient for all times, for certain smooth and compactly supported initial vorticity in $\mathbb{R}^2$. The construction carries over to some generalized SQG equations.

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Kyudong Choi, In-Jee Jeong. 2021-08-04. Infinite growth in vorticity gradient of compactly supported planar vorticity near Lamb dipole. https://arxiv.org/abs/2108.01811

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