Global solutions for the gravity water waves equation in dimension 3

• 成果类型: Article
• 署名作者: Germain, P.; Masmoudi, N.; Shatah, J.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2012.175.2.6
• 发表日期: 2012
• 页码: 691-754
• 关键词: well-posedness; surface-tension; sobolev spaces; motion; fluid

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.