Institute of Mathematics


Modul:   MAT673  Seminar PDE and Mathematical Physics

Standing gravity capillary water waves

Pietro Baldi talk

Speaker invited by: Prof. Dr. Thomas Kappeler

Date: 26.02.15  Time: 18.15 - 19.15  Room: Y27H35/36

Abstract: In this talk I will present a recent work in collaboration with Thomas Alazard (ENS-Paris). We consider 2D gravity-capillary water waves equations in their Hamiltonian formulation, and we address the question of the nonlinear interaction of a plane wave with its reflection off a vertical wall. The main result is the construction of small amplitude, standing (namely periodic in time and space, and not travelling) solutions of Sobolev regularity, for almost all values of the surface tension coefficient, and for a large set of time-frequencies. This is an existence result for a quasi-linear, Hamiltonian, reversible system of two autonomous pseudo-PDEs with small divisors. The proof is a combination of different techniques, such as a Nash-Moser scheme, microlocal analysis, and bifurcation analysis.