Non-existence of cusps for a Free-boundary Problem for Water Waves

2022/08/03 by Sean McCurdy, McCurdy, Sean
Mathematics · #35R35 #76B15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2208.01873

openalex publication_date 2022/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In arXiv:0908.1031, Varvaruca and Weiss eliminate the existence of cusps for a free-boundary problem for two-dimensional water waves under assumptions that hold for solutions such that \u>0\ is a "strip-like" domain in the sense of arXiv:0708.4371. In this paper it is proven that cusps do not exists in the natural setting for these free-boundary problems. In particular, non strip-like domains are also allowed. This builds upon recent work on non-existence of cusps in arXiv:2202.00616.

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