Title: The water waves problem

Abstract: We will begin by introducing the water waves equations, which are a system of nonlinear PDEs modeling the motion of fluids with free moving boundaries, such as waves on the surface of the ocean.

We will then discuss several works done on this system in recent years and how they fit into the broader context of the study of nonlinear evolution problems. Eventually we will present some of our main results, obtained in collaboration with Ionescu and Deng-Ionescu-Pausader, on the global regularity of solutions.