Abstract:
We study the motion of a compressible perfect liquid body in vacuum. This can be through 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 linearized stability in Sobolev space assuming a ``physical condition'', related to the fact that the pressure of a fluid has to be positive.
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Received: 23 September 2002 / Accepted: 2 December 2002 Published online: 14 April 2003
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ID="⋆" The author was supported in part by the National Science Foundation.
Communicated by P. Constantin
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Lindblad, H. Well-Posedness for the Linearized Motion of a Compressible Liquid with Free Surface Boundary. Commun. Math. Phys. 236, 281–310 (2003). https://doi.org/10.1007/s00220-003-0812-x
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DOI: https://doi.org/10.1007/s00220-003-0812-x