ArticleOriginal scientific text
Title
Local existence of solutions of the free boundary problem for the equations of compressible barotropic viscous self-gravitating fluids
Authors 1, 2
Affiliations
- Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242, U.S.A.
- Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland
Abstract
Local existence of solutions is proved for equations describing the motion of a viscous compressible barotropic and self-gravitating fluid in a domain bounded by a free surface. First by the Galerkin method and regularization techniques the existence of solutions of the linearized momentum equations is proved, next by the method of successive approximations local existence to the nonlinear problem is shown.
Keywords
compressible viscous barotropic self-gravitating fluids, local existence
Bibliography
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- V. A. Solonnikov, On nonstationary motion of a bounded isolated mass of a selfgravitating fluid, Algebra i Analiz 1 (1989), 207-249 (in Russian).
- G. Ströhmer and W. M. Zajączkowski, On stability of equilibrium solution for compressible barotropic viscous self-gravitating fluid motions bounded by a free surface, to appear.
- W. M. Zajączkowski, Existence of local solutions for free boundary problems for viscous compressible barotropic fluid, Ann. Polon. Math. 60 (1995), 255-287.
- W. M. Zajączkowski, On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface, Dissertationes Math. 324 (1993).
Pages:
1-31
Main language of publication
English
Received
1998-04-27
Published
1999
Exact and natural sciences