On two-dimensional gravity water waves with angled crests
Sijue Wu (University of Michigan)
MSRI: Simons Auditorium
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 $E(0)<\infty$, there is $T>0$, 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.