The Analysis and PDE Seminar will take place on Monday, November 14th, in room 740, Evans Hall, from 4:10-5:00 pm.

Title: Finite depth gravity water waves In holomorphic coordinates

Abstract: In this article we consider irrotational gravity water waves with finite bottom. Our goal is two-fold. First, we represent the equations in holomorphic coordinates and discuss the local well-posedness of the problem in this context. Second, we consider the small data problem and establish cubic lifespan bounds for the solutions. Our results are uniform in the infinite depth limit, and match our earlier infinite depth paper.