Videos

Control of water waves

Presenter
October 27, 2015
Keywords:
  • water waves in a tank
  • generating water waves
  • gravity-capillary interactions
  • finite boundary condition
  • local data
  • quasi-linear PDE
MSC:
  • 76B15
  • 35A01
  • 35B30
Abstract
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.
Supplementary Materials