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

G. Ströhmer; W. Zajączkowski

Applicationes Mathematicae (1999)

  • Volume: 26, Issue: 1, page 1-31
  • ISSN: 1233-7234

Abstract

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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.

How to cite

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Ströhmer, G., and Zajączkowski, W.. "Local existence of solutions of the free boundary problem for the equations of compressible barotropic viscous self-gravitating fluids." Applicationes Mathematicae 26.1 (1999): 1-31. <http://eudml.org/doc/219224>.

@article{Ströhmer1999,
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.},
author = {Ströhmer, G., Zajączkowski, W.},
journal = {Applicationes Mathematicae},
keywords = {compressible viscous barotropic self-gravitating fluids; local existence; local existence of solutions; viscous compressible barotropic self-gravitating fluid; free surface; Galerkin method; regularization; linearized momentum equations; method of successive approximations},
language = {eng},
number = {1},
pages = {1-31},
title = {Local existence of solutions of the free boundary problem for the equations of compressible barotropic viscous self-gravitating fluids},
url = {http://eudml.org/doc/219224},
volume = {26},
year = {1999},
}

TY - JOUR
AU - Ströhmer, G.
AU - Zajączkowski, W.
TI - Local existence of solutions of the free boundary problem for the equations of compressible barotropic viscous self-gravitating fluids
JO - Applicationes Mathematicae
PY - 1999
VL - 26
IS - 1
SP - 1
EP - 31
AB - 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.
LA - eng
KW - compressible viscous barotropic self-gravitating fluids; local existence; local existence of solutions; viscous compressible barotropic self-gravitating fluid; free surface; Galerkin method; regularization; linearized momentum equations; method of successive approximations
UR - http://eudml.org/doc/219224
ER -

References

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  1. [1] L. Landau and E. Lifschitz, Hydrodynamics, Nauka, Moscow, 1986 (in Russian); English transl.: Fluid Mechanics, Pergamon Press, Oxford, 1987. 
  2. [2] P. Secchi, On the evolution equations of viscous gaseous stars, Ann. Scuola Norm. Sup. Pisa 18 (1991), 295-318. Zbl0761.35117
  3. [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). Zbl0713.76044
  4. [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. Zbl1016.76065
  5. [5] W. M. Zajączkowski, Existence of local solutions for free boundary problems for viscous compressible barotropic fluid, Ann. Polon. Math. 60 (1995), 255-287. Zbl0923.35134
  6. [6] W. M. Zajączkowski, On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface, Dissertationes Math. 324 (1993). Zbl0771.76059

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