University of California at San Diego
The Motion of the Free
Surface of a Liquid 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.