On the Cauchy problem for gravity water waves

• 成果类型: Article
• 署名作者: Alazard, T.; Burq, N.; Zuily, C.
• 署名单位: Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0498-z
• 发表日期: 2014
• 页码: 71-163
• 关键词: well-posedness; free-surface; sobolev spaces; EQUATIONS; SINGULARITIES; EXISTENCE; calculus; motion

摘要

We are interested in the system of gravity water waves equations without surface tension. Our purpose is to study the optimal regularity thresholds for the initial conditions. In terms of Sobolev embeddings, the initial surfaces we consider turn out to be only of -class for some and consequently have unbounded curvature, while the initial velocities are only Lipschitz. We reduce the system using a paradifferential approach.