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 -