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.

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Speaker:  Sijue Wu
Institution:  Umich

Event Organizer:     

 

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