On the motion of water waves with angled crests

In this talk, I will discuss recent progress concerning the solutions of the full water wave equation, for any data that allows for angled crested interfaces. We will show that the water wave equation is locally well-posed in a regime that allows for angled crested interfaces. We will also show that for any data of size $\epsilon$ that allows for angled crests, the life span of the solution is at least of order $O(\epsilon^{-3})$.