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

Alexander Kiselev; Xiaoyutao Luo

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

Analysis of PDEs 2021-12-06 v2

Authors: Alexander Kiselev , Xiaoyutao Luo

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.

Keywords

alpha-SQG equation patch solutions splash singularity curvature lower bound finite-time collision

Cite

@article{arxiv.2111.13794,
  title  = {On nonexistence of splash singularities for the $\alpha$-SQG patches},
  author = {Alexander Kiselev and Xiaoyutao Luo},
  journal= {arXiv preprint arXiv:2111.13794},
  year   = {2021}
}

Comments

12 pages; corrected some exponents

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