Date: Thursday, November 12, 2015
Location: 4088 East Hall (4:00 PM to 5:00 PM)
Title: On twodimensional gravity water waves with angled crests
Abstract: We consider the twodimensional water wave problem in the case where the free interface of the fluid meets a vertical wall at a possibly nonright 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 lowregularity energy and prove a closed energy estimate for this problem, and we show that the twodimensional 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.
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Speaker: Sijue Wu
Institution: Umich
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