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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Explore related subjectsDiscover the latest articles and news from researchers in related subjects, suggested using machine learning. Author information Authors and AffiliationsDepartment of Mathematics, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0112, USA. E-mail: lindblad@math.ucsd.edu, , , , , , US
Hans Lindblad
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
About this article Cite this articleLindblad, 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
Issue Date: May 2003
DOI: https://doi.org/10.1007/s00220-003-0812-x
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