Geodesic
Non-existence of cusps for a free-boundary problem for water waves
Sean McCurdy1 orcid
1National Taiwan Normal University, Taipei, Taiwan
Interfaces and free boundaries, Tome 27 (2025) no. 1, pp. 1-11

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DOI

In Varvaruca and Weiss (2011), Varvaruca and Weiss eliminate the existence of cusps for a free-boundary problem for two-dimensional water waves under assumptions that hold for solutions for which {u>0} is a “strip-like” domain in the sense of Varvaruca (2008). In this paper, it is proven that cusps do not exist in the natural setting for these free-boundary problems. In particular, non-strip-like domains are also allowed. This qualitative result follows from quantitative results which, roughly speaking, give lower bounds on the “slope” at which the free boundary approaches a stagnation point. This builds upon recent work on non-existence of cusps in McCurdy and Naples (2022) for local minimizers.
DOI : 10.4171/ifb/527
Classification : 35R35, 76B15
Mots-clés : Stokes wave, partial regularity, cusps

Sean McCurdy  1

1 National Taiwan Normal University, Taipei, Taiwan 
Sean McCurdy. Non-existence of cusps for a free-boundary problem for water waves. Interfaces and free boundaries, Tome 27 (2025) no. 1, pp. 1-11. doi: 10.4171/ifb/527
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