CRM CAMP in Nonlinear Analysis

Computer-Assisted Mathematical Proofs in Nonlinear Analysis

July 14, 2020 from 10:00 to 11:00 (Montreal/EST time) Zoom meeting

Uniqueness of Whitham's highest cusped wave

Seminar presented by Javier Gómez-Serrano (Brown University, USA & University of Barcelona, Spain)

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.