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Global Regularity for 2d Water Waves with Surface Tension
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eBook
Global Regularity for 2d Water Waves with Surface Tension
2018
Overview
We consider the full irrotational water waves system with surface tension and no gravity in dimension two (the capillary waves
system), and prove global regularity and modified scattering for suitably small and localized perturbations of a flat interface. An
important point of our analysis is to develop a sufficiently robust method, based on energy estimates and dispersive analysis, which
allows us to deal simultaneously with strong singularities arising from time resonances in the applications of the normal form method
and with nonlinear scattering. As a result, we are able to consider a suitable class of perturbations with finite energy, but no other
momentum conditions.
Part of our analysis relies on a new treatment of the Dirichlet-Neumann operator in dimension two which is
of independent interest. As a consequence, the results in this paper are self-contained.
Publisher
American Mathematical Society
Subject
ISBN
9781470431037, 1470431033
