Math @ Duke
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Publications [#365620] of Xiaoyutao Luo
Papers Published
- Kiselev, A; Luo, X, On nonexistence of splash singularities for the $α$-SQG patches
(November, 2021)
(last updated on 2023/07/05)
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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