Erik Wahlén

Global weak solutions of the Camassa-Holm equation

DIFTA 2005–05–13

Abstract: The Camassa–Holm equation is a nonlinear partial differential equation that models shallow water waves. I will discuss the role of the momentum variable m=uuxx for the global existence of solutions of this equation. For classical solutions it is known that if initially the negative part of m lies completely to left of the positive part, then the corresponding solution is globally defined in time. I will present a generalization of this result to weak solutions. The solutions thus obtained are unique in a certain class.