Convexity of Whitham's highest cusped wave

2018/10/25 by Alberto Enciso, Javier Gómez-Serrano, Enciso, Alberto +3 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1810.10935

32 pages, preliminary version

arxiv created 2018/10/25 · arxiv updated 2018/10/26

Abstract

We prove the existence of a periodic traveling wave of extreme form of the Whitham equation that has a convex profile between consecutive stagnation points, at which it is known to feature a cusp of exactly C^1/2 regularity. The convexity of Whitham's highest cusped wave had been conjectured by Ehrnström and Wahlén.

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