TY - JOUR
T1 - Global solutions for the gravity water waves equation in dimension 3
AU - Germain, P.
AU - Masmoudi, Nader
AU - Shatah, Jalal
PY - 2009/8
Y1 - 2009/8
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. To cite this article: P. Germain et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).
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. To cite this article: P. Germain et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).
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U2 - 10.1016/j.crma.2009.05.005
DO - 10.1016/j.crma.2009.05.005
M3 - Article
AN - SCOPUS:67650725448
SN - 1631-073X
VL - 347
SP - 897
EP - 902
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 15-16
ER -