Well posedness for the motion of a compressible liquid with free surface boundary

Details Well posedness for the motion of a compressible liquid with free surface boundary Well posedness for the motion of a compressible liquid with free surface boundary

2005-04-16

arxiv.org/abs/math/0504339v1

Mathematics

Analysis of PDEs

to appear in CMP

Scientific paper

10.1007/s00220-005-1406-6

We study the motion of a compressible 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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