Well-posedness for the Motion of an Incompressible Liquid with Free Surface Boundary

@inproceedings{Lindblad2004WellposednessFT,
  title={Well-posedness for the Motion of an Incompressible Liquid with Free Surface Boundary},
  author={Hans Lindblad},
  year={2004}
}
Abstract. 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… CONTINUE READING
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