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ArticleOriginal scientific text

Title

Existence of local solutions for free boundary problems for viscous compressible barotropic fluids

Authors 1

Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, P.O. Box 137, 00-950 Warszawa, Poland

Abstract

We prove the local existence of solutions for equations of motion of a viscous compressible barotropic fluid in a domain bounded by a free surface. The solutions are shown to exist in exactly those function spaces where global solutions were found in our previous papers [14, 15].

Keywords

ENG
local existence, free boundary, anisotropic Sobolev spaces, viscous compressible barotropic fluids

Bibliography

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  9. E. Zadrzyńska and W. M. Zajączkowski, On local motion of a general compressible viscous heat conducting fluid bounded by a free surface, Ann. Polon. Math. 59 (1994), 133-170.
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  11. E. Zadrzyńska and W. M. Zajączkowski, On the global existence theorem for a free boundary problem for equations of a viscous compressible heat conducting capillary fluid, to appear.
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  13. W. M. Zajączkowski, On local motion of a compressible barotropic viscous fluid bounded by a free surface, in: Banach Center Publ. 27, Inst. Math., Polish Acad. Sci., 1992, 511-553.
  14. W. M. Zajączkowski, On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface, Dissertationes Math. 324 (1993).
  15. W. M. Zajączkowski, On nonstationary motion of a compressible barotropic viscous capillary fluid bounded by a free surface, SIAM J. Math. Anal. 25 (1994), 1-84.
Annales Polonici Mathematici
1994-1995/60/3
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Pages:
255-287
Main language of publication
English
Received
1993-11-03
Accepted
1994-03-15
Published
1995
Exact and natural sciences