Nastasia Grubic: On the angle-crested water waves and singularity formation

Abstract:

In the first part of the talk we discuss a local well-posedness result in a class of weighted Sobolev spaces that allows propagation of angled-crests on the interface. As a consequence of the asymptotic characterization of the fluid dynamics at the crest tip, we obtain a decoupled system of ODE’s whose solutions blow-up in finite time. In the second part we discuss how this leads to singularity formation for the full system, and in particular how the local existence result has to be augmented in order to extend the solutions up to the blow-up time. This is based on a joint work with D. Cordoba and A. Enciso.