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On two-dimensional gravity water waves with angled crests

New challenges in PDE: Deterministic dynamics and randomness in high and infinite dimensional systems October 19, 2015 - October 30, 2015

October 21, 2015 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Sijue Wu (University of Michigan)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • Local well-posedness results

  • Energy functional

  • Water wave modelling

  • Low-regularity Sobolev space

  • singularities

  • Self-similar solutions

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

14377

Abstract

In this talk, I will present our recent work on the local in time existence of two-dimensional gravity water waves with angled crests. Specifically,  we construct an energy functional $E(t)$ that allows for angled crests in the interface. We show that for any initial data satisfying $E(0)<\infty$, there is $T>0$, depending only on $E(0)$, such that the water wave system is solvable for time $t\in [0, T]$. Furthermore we show that for any smooth initial data, the unique solution of the 2d water wave system remains smooth so long as $E(t)$ remains finite.

Supplements
24938?type=thumb Wu_Notes 500 KB application/pdf Download
Video/Audio Files

14377

H.264 Video 14377.mp4 326 MB video/mp4 rtsp://videos.msri.org/data/000/024/580/original/14377.mp4 Download
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