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

Hans Lindblad

Type: Article

Publication Date: 2005-07-01

Citations: 321

DOI: https://doi.org/10.4007/annals.2005.162.109

Abstract

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.

Locations

arXiv (Cornell University) - View - PDF
CiteSeer X (The Pennsylvania State University) - View - PDF
Annals of Mathematics - View - PDF

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