Videos

On two-dimensional gravity water waves with angled crests

Presenter
October 20, 2015
Keywords:
  • Local well-posedness results
  • Energy functional
  • Water wave modelling
  • Low-regularity Sobolev space
  • singularities
  • Self-similar solutions
MSC:
  • 35J60
  • 35Q86
  • 35Q35
  • 76N10
  • 76B15
Abstract
In this talk, I will present our recent work on the local in time existence of two-dimensional gravity water waves with angled crests. Specifically, we construct an energy functional $E(t)$ that allows for angled crests in the interface. We show that for any initial data satisfying $E(0)0$, depending only on $E(0)$, such that the water wave system is solvable for time $t\in [0, T]$. Furthermore we show that for any smooth initial data, the unique solution of the 2d water wave system remains smooth so long as $E(t)$ remains finite.
Supplementary Materials