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


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.


Hans Lindblad

Department of Mathematics, University of California at San Diego, La Jolla, CA 92093, United States