Global solutions for the gravity water waves equation in dimension 3

• Autores: Pierre Germain, N. Masmoudi , Jalal Shatah
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 175, Nº 2, 2012, págs. 691-754
• Idioma: inglés
• DOI: 10.4007/annals.2012.175.2.6
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• Resumen

  • 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 8 . To obtain these dispersive estimates, we use an analysis in Fourier space; the study of space and time resonances is then the crucial point.