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

Analysis of PDEs 2007-05-23 v1 Mathematical Physics math.MP

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 fluid has to be positive.

Keywords

Cite

@article{arxiv.math/0402327,
  title  = {Well-posedness for the motion of an incompressible liquid with free surface boundary},
  author = {Hans Lindblad},
  journal= {arXiv preprint arXiv:math/0402327},
  year   = {2007}
}

Comments

To appear in the Annals of Math