Variational aspects of steady irrotational water wave theory

Abstract: Among the many modern approaches to abstract nonlinear problems, those based on the implicit function theorem, real-analytic function theory, Nash-Moser theory and topological degree theory have made significant contributions to water-wave theory in recent years. However, the same cannot be said of variational methods (min/max, mountain-pass, Morse index, Lyusternik-Schnirelman genus etc) even though, when the viscosity of water is ignored and the flow is assumed to be irrotational, there are several attractive ways to formulate the equations of wave motion variationally. On the 100th anniversary of the first proof that the equations of motion have non-zero, small-amplitude solutions, this talk will briefly survey these issues and advocate variational methods for analyzing water waves that are 2π-periodic in space.

analysis of PDEsclassical analysis and ODEs

Audience: researchers in the topic

Online Northeast PDE and Analysis Seminar