Videos

Global stability of a flat interface for the gravity-capillary water-wave model

Presenter
October 26, 2015
Keywords:
  • Wave equation
  • gravity interaction
  • surface tension, capillary action
  • Water wave modelling
  • coupling
  • dispersive PDEs
  • long range behavior
MSC:
  • 76B15
  • 76B03
  • 35Q35
  • 35B40
  • 35B30
  • 35B20
  • 74Gxx
Abstract
The water wave model describes the evolution of a flat interface between air and an inviscid, incompressible fluid. It is known that (in 3D), if one considers the action of either gravity or surface tension alone, small localized perturbations of a flat interface lead to global solutions that scatter back to equilibrium, in a joint work with Y. Deng, A. Ionescu and F. Pusateri, we show that this remains true when one considers both forces.
Supplementary Materials