Uniqueness of Whitham's highest cusped wave

Abstract: Whitham’s equation of shallow water waves is a non-homogeneous non-local dispersive equation. As in the case of the Stokes wave for the Euler equation, non-smooth traveling waves with greatest height between crest and trough have been shown to exist. In this talk I will discuss uniqueness of solutions to the Whitham equation and show that there exists a unique, even and periodic traveling wave of greatest height, that moreover has a convex profile between consecutive stagnation points, at which there is a cusp. Joint work with Alberto Enciso and Bruno Vergara.

analysis of PDEsclassical analysis and ODEsdynamical systemsfunctional analysisnumerical analysis

Audience: researchers in the discipline

( video )

CRM CAMP (Computer-Assisted Mathematical Proofs) in Nonlinear Analysis

Series comments: To have access to the zoom details of the talks, please register at www.crm.math.ca/camp-nonlinear