Cusp Formation in Vortex Patches

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arxiv 2504.02705 v2 pith:R3IRZWTO submitted 2025-04-03 math.AP

Tarek M. Elgindi , Min Jun Jo This is my paper · ORCID

classification math.AP

keywords cuspformationvortexacuteconjecturedcornersinitialinstantaneous

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We prove instantaneous cusp formation for any initial vortex patch with acute corners. This was conjectured to occur in the numerical literature.

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Uniformly Rotating Vortex Patches with 90-Degree Corners
math.AP 2026-08 conditional novelty 8.0 of 10

For every m at least 12, there exist m-fold symmetric uniformly rotating vortex patches whose boundaries have exactly m right-angle corners, proved by a new fixed-point construction.