Global solutions for the gravity water waves equation in dimension 3

被引：217

作者：

Germain, P. ^{[1
]}

Masmoudi, N. ^{[1
]}

Shatah, J. ^{[1
]}

机构：

[1] NYU, Courant Inst Math Sci, New York, NY 10003 USA

来源：

ANNALS OF MATHEMATICS | 2012年 / 175卷 / 02期

基金：

美国国家科学基金会;

关键词：

WELL-POSEDNESS; SURFACE-TENSION; SOBOLEV SPACES; MOTION; FLUID;

D O I：

10.4007/annals.2012.175.2.6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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

引用

页码：691 / 754

页数：64

共 31 条

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Ambrose DM, 2007, COMMUN MATH SCI, V5, P391

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