Finite time singularities for the free boundary incompressible Euler equations

• 成果类型: Article
• 署名作者: Castro, Angel; Cordoba, Diego; Fefferman, Charles; Gancedo, Francisco; Gomez-Serrano, Javier
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2013.178.3.6
• 发表日期: 2013
• 页码: 1061-1134
• 关键词: water-waves equation; well-posedness; free-surface; interface evolution; global-solutions; sobolev spaces; muskat problem; motion; EXISTENCE; breakdown

摘要

In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible Euler equations (also known for some particular scenarios as the water wave problem) for which the smoothness of the interface breaks down in finite time into a splash singularity or a splat singularity.