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Control of water waves

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

October 27, 2015 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Thomas Alazard (École Normale Supérieure; Centre National de la Recherche Scientifique (CNRS))
Location: MSRI: Simons Auditorium
  • water waves in a tank

  • generating water waves

  • gravity-capillary interactions

  • finite boundary condition

  • local data

  • quasi-linear PDE

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



Water waves are disturbances of the free surface of a liquid. They are, in general, produced

by the immersion of a solid body or by impulsive pressures applied on the free surface. The 

two questions we discuss in this talk are the following: 

- which waves can be generated by blowing on a localized portion of the free surface ? 

Our main result with Pietro Baldi and Daniel Han-Kwan asserts that one can generate any small amplitude, periodic in x, two-dimensional, gravity-capillary water waves. 

- consider now gravity water waves in a rectangular tank. Is-it possible to estimate their energy by

looking only at the motion of some of the curves of contact between the free surface and the vertical walls

24871?type=thumb Alazard-Notes 50.2 KB application/pdf Download
24872?type=thumb Alazard-Talk 377 KB application/pdf Download
Video/Audio Files


H.264 Video 14390.mp4 285 MB video/mp4 rtsp://videos.msri.org/data/000/024/652/original/14390.mp4 Download
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