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arXiv · 2111.13794

On nonexistence of splash singularities for the $\alpha$-SQG patches

Alexander Kiselev·Xiaoyutao Luo
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Abstract

In this paper, we consider patch solutions to the $\alpha$-SQG equation and derive new criteria for the absence of splash singularity where different patches or parts of the same patch collide in finite time. Our criterion refines a result due to Gancedo and Strain \cite{GS}, providing a condition on the growth of curvature of the patch necessary for the splash and an exponential in time lower bound on the distance between patches with bounded curvature.

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Alexander Kiselev, Xiaoyutao Luo. 2021-11-27. On nonexistence of splash singularities for the $\alpha$-SQG patches. https://arxiv.org/abs/2111.13794

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