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

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