Global Solutions for the Gravity Water Waves Equation in Dimension 3

Details Global Solutions for the Gravity Water Waves Equation in Dimension 3 Global Solutions for the Gravity Water Waves Equation in Dimension 3

2009-06-29

arxiv.org/abs/0906.5343v1

Mathematics

Analysis of PDEs

Scientific paper

We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L^2 related norms, with dispersive estimates, which give decay in L^\infty. To obtain these dispersive estimates, we use an analysis in Fourier space; the study of space and time resonances is then the crucial point.

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