One World Waves - B Vergara
From OLLIE Quinn on July 16th, 2020
Bruno Vergara: Uniqueness and convexity of Whitham’s highest cusped wave.
The Whitham equation is a non-local, non-homogeneous and weakly dispersive model for shallow water waves. Like in the case of the Stokes wave for Euler, non-smooth traveling waves with greatest height between crest and trough have been shown to exist for this model. In this talk I will discuss the existence of a unique, even and periodic traveling wave of greatest height solution to the Whitham equation. This wave of extreme form is unique in the class of monotone solutions and, moreover, it is convex between consecutive cusps. The talk is based on a joint work with A. Enciso and J. Gómez-Serrano.