Local existence of solutions of the free boundary problem for the equations of compressible barotropic viscous self-gravitating fluids

• Autorzy: G. Ströhmer , W. M. Zajączkowski
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

compressible viscous barotropic self-gravitating fluids; local existence

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1999
• Tom: 26
• Numer: 1
• Strony: 1-31

Daty

wydano

1999

otrzymano

1998-04-27

Twórcy

autor

G. Ströhmer

• Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242, U.S.A.

autor

W. M. Zajączkowski

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland

Bibliografia

• [1] L. Landau and E. Lifschitz, Hydrodynamics, Nauka, Moscow, 1986 (in Russian); English transl.: Fluid Mechanics, Pergamon Press, Oxford, 1987.
• [2] P. Secchi, On the evolution equations of viscous gaseous stars, Ann. Scuola Norm. Sup. Pisa 18 (1991), 295-318.
• [3] V. A. Solonnikov, On nonstationary motion of a bounded isolated mass of a selfgravitating fluid, Algebra i Analiz 1 (1989), 207-249 (in Russian).
• [4] 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.
• [5] W. M. Zajączkowski, Existence of local solutions for free boundary problems for viscous compressible barotropic fluid, Ann. Polon. Math. 60 (1995), 255-287.
• [6] W. M. Zajączkowski, On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface, Dissertationes Math. 324 (1993).