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

Applicationes Mathematicae (1999)

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

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topStröhmer, 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

top- [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. Zbl0761.35117
- [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] 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] 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] 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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