The Analysis and PDE seminar will take place Monday, October 9nd, in 740 Evans from 4:10 to 5pm.
Title: Gravity water waves and emerging bottom
Abstract: To understand the behavior of waves at a fluid surface in configurations where the surface and the bottom meet (islands, beaches…), one encounters a difficulty: the presence in the bulk of the fluid of an edge, at the triple line. To solve the Cauchy problem, we need to study elliptic regularity in such domains, understand the linearized operator around an arbitrary solution, and construct an appropriate procedure to quasi-linearize the equations. Using those tools, I will present some a priori estimates, a first step to a local existence result.