Global stability of a flat interface for the gravity-capillary water-wave model
New challenges in PDE: Deterministic dynamics and randomness in high and infinite dimensional systems October 19, 2015 - October 30, 2015
Location: MSRI: Simons Auditorium
Water wave modelling
long range behavior
76B15 - Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30]
76B03 - Existence, uniqueness, and regularity theory [See also 35Q35]
35B30 - Dependence of solutions on initial and boundary data, parameters [See also 37Cxx]
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.
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