2005/04/16 by Hans Lindblad · 1 citation
Mathematics · Physics and Astronomy · #math.AP #math-ph #math.MP
paper · pdf · doi:10.1007/s00220-005-1406-6
to appear in CMP
arxiv created 2005/04/16 · arxiv updated 2009/12/01
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.