TY - JOUR

T1 - Global solutions for the gravity water waves equation in dimension 3

AU - Germain, P.

AU - Masmoudi, N.

AU - Shatah, J.

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2012/3

Y1 - 2012/3

N2 - 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 L2 related norms, with dispersive estimates, which give decay in L∞. To obtain these dispersive estimates, we use an analysis in Fourier space; the study of space and time resonances is then the crucial point.

AB - 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 L2 related norms, with dispersive estimates, which give decay in L∞. 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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U2 - 10.4007/annals.2012.175.2.6

DO - 10.4007/annals.2012.175.2.6

M3 - Article

AN - SCOPUS:84857870242

SN - 0003-486X

VL - 175

SP - 691

EP - 754

JO - Annals of Mathematics

JF - Annals of Mathematics

IS - 2

ER -