# Seminar Event Detail

Differential Equations

 Date:  Thursday, November 12, 2015 Location:  4088 East Hall (4:00 PM to 5:00 PM) Title:  On two-dimensional gravity water waves with angled crests Abstract:   We consider the two-dimensional water wave problem in the case where the free interface of the fluid meets a vertical wall at a possibly non-right angle; our problem also covers interfaces with angled crests. We assume that the fluid is inviscid, incompressible, and irrotational, with no surface tension and with air density zero. We construct a low-regularity energy and prove a closed energy estimate for this problem, and we show that the two-dimensional water wave problem is solvable locally in time in this framework. Our work differs from earlier work in that, in our case, only a degenerate Taylor stability criterion holds, with $-\frac{\partial P}{\partial \bold{n}} \ge 0$, instead of the strong Taylor stability criterion $-\frac{\partial P}{\partial \bold{n}} \ge c > 0$. This work is partially joint with Rafe Kinsey. Files: Speaker:  Sijue Wu Institution:  Umich Event Organizer: