Well-posedness for the motion of an incompressible liquid with free surface boundary

• 成果类型: Article
• 署名作者: Lindblad, H
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2005.162.109
• 发表日期: 2005
• 页码: 109-194
• 关键词: water-wave problem; linearized motion; sobolev spaces

摘要

We study the motion of an incompressible perfect liquid body in vacuum. This can be thought of as a model for the motion of the ocean or a star. The free surface moves with the velocity of the liquid and the pressure vanishes on the free surface. This leads to a free boundary problem for Euler's equations, where the regularity of the boundary enters to highest order. We prove local existence in Sobolev spaces assuming a physical condition, related to the fact that the pressure of a fluid has to be positive.