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

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

2004-02-20

arxiv.org/abs/math/0402327v1

Mathematics

Analysis of PDEs

To appear in the Annals of Math

Scientific paper

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.

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