Wellposedness of the 2D full water wave equation in a regime that allows for non-C1 interfaces

• 成果类型: Article
• 署名作者: Wu, Sijue
• 署名单位: University of Michigan System; University of Michigan
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-019-00867-4
• 发表日期: 2019
• 页码: 241-375
• 关键词: free-boundary problem; well-posedness; free-surface; global-solutions; sobolev spaces; motion; fluid

摘要

We consider the two dimensional gravity water wave equation in a regime where the free interface is allowed to be non-C-1. In this regime, only a degenerate Taylor inequality -partial derivative P/partial derivative n >= 0 holds, with degeneracy at the singularities. In Kinsey and Wu (Camb J Math 6(2):93-181, 2018) an energy functional E(t) was constructed and an a-priori estimate was proved. The energy functional E(t) is not only finite for interfaces and velocities in Sobolev spaces, but also finite for a class of non-C1 interfaces with angled crests. In this paper we prove the existence, uniqueness and stability of the solution of the 2d gravity water wave equation in the class where E(t)