Wellposedness and singularities of the water wave equations

Abstract

A class of water wave problems concerns the dynamics of the free interface separating an inviscid, incompressible and irrotational fluid, under the influence of gravity, from a zero-density region. In this note, we present some recent methods and ideas developed concerning the local and global wellposedness of these problems, the focus is on the structural aspect of the equations.

This is the lecture notes for a short course given at the Newton Institute, Cambridge in August 2014

References in corpus (2)

• A blow-up criteria and the existence of 2d gravity water waves with angled crests
• Nonstandard estimates for a class of 1D dispersive equations and applications to linearized water waves

Cited by in corpus (1)

• On the transition of the Rayleigh-Taylor instability in 2d water waves