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

Annales Polonici Mathematici (1995)

- Volume: 60, Issue: 3, page 255-287
- ISSN: 0066-2216

## Access Full Article

top## Abstract

top## How to cite

topW. M. Zajączkowski. "Existence of local solutions for free boundary problems for viscous compressible barotropic fluids." Annales Polonici Mathematici 60.3 (1995): 255-287. <http://eudml.org/doc/262333>.

@article{W1995,

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].},

author = {W. M. Zajączkowski},

journal = {Annales Polonici Mathematici},

keywords = {local existence; free boundary; anisotropic Sobolev spaces; viscous compressible barotropic fluids; Navier-Stokes equations; time-dependent boundary; surface tension; iterations; anisotropic Sobolev-Slobodetskij spaces},

language = {eng},

number = {3},

pages = {255-287},

title = {Existence of local solutions for free boundary problems for viscous compressible barotropic fluids},

url = {http://eudml.org/doc/262333},

volume = {60},

year = {1995},

}

TY - JOUR

AU - W. M. Zajączkowski

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

JO - Annales Polonici Mathematici

PY - 1995

VL - 60

IS - 3

SP - 255

EP - 287

AB - 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].

LA - eng

KW - local existence; free boundary; anisotropic Sobolev spaces; viscous compressible barotropic fluids; Navier-Stokes equations; time-dependent boundary; surface tension; iterations; anisotropic Sobolev-Slobodetskij spaces

UR - http://eudml.org/doc/262333

ER -

## References

top- [1] O. V. Besov, V. P. Il'in and S. M. Nikol'skiĭ, Integral Representation of Functions and Imbedding Theorems, Nauka, Moscow, 1975 (in Russian).
- [2] D. K. Faddeev, V. A. Solonnikov and N. N. Ural'tseva, Selected Topics of Analysis and Algebra, Leningrad, 1981 (in Russian).
- [3] O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type, Nauka, Moscow, 1967 (in Russian).
- [4] L. Landau and E. Lifschitz, Mechanics of Continuum Media, Nauka, Moscow, 1954 (in Russian); English transl.: Pergamon Press, Oxford, 1959; new edition: Hydrodynamics, Nauka, Moscow, 1986 (in Russian).
- [5] V. A. Solonnikov, On an initial-boundary value problem for the Stokes system which appears in free boundary problems, Trudy Mat. Inst. Steklov. 188 (1990), 150-188 (in Russian).
- [6] V. A. Solonnikov, On boundary problems for linear parabolic systems of differential equations of general form, ibid. 83 (1965) (in Russian). Zbl0164.12502
- [7] V. A. Solonnikov, A priori estimates for second order parabolic equations, ibid. 70 (1964), 133-212 (in Russian). Zbl0168.08202
- [8] V. A. Solonnikov and A. Tani, Free boundary problem for a viscous compressible flow with a surface tension, in: Constantine Carathéeodory: An International Tribute, T. M. Rassias (ed.), World Scientific, 1991, 1270-1303. Zbl0752.35096
- [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. Zbl0812.35102
- [10] E. Zadrzyńska and W. M. Zajączkowski, On the global existence theorem for a free boundary problem for equations of a viscous compressible heat conducting fluid, to appear. Zbl0874.35097
- [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. Zbl0874.35097
- [12] W. M. Zajączkowski, On an initial-boundary value problem for the parabolic system which appears in free boundary problems for compressible Navier-Stokes equations, Dissertationes Math. 304 (1990).
- [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. Zbl0791.35105
- [14] W. M. Zajączkowski, On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface, Dissertationes Math. 324 (1993). Zbl0771.76059
- [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. Zbl0813.35086

## Citations in EuDML Documents

top- G. Ströhmer, W. Zajączkowski, Local existence of solutions of the free boundary problem for the equations of compressible barotropic viscous self-gravitating fluids
- Ewa Zadrzyńska, Wojciech M. Zajączkowski, On a differential inequality for equations of a viscous compressible heat conducting fluid bounded by a free surface
- Ewa Zadrzyńska, Wojciech M. Zajączkowski, On the global existence theorem for a free boundary problem for equations of a viscous compressible heat conducting fluid
- Ewa Zadrzyńska, Wojciech Zajączkowski, On nonstationary motion of a fixed mass of a viscous compressible barotropic fluid bounded by a free boundary
- Ewa Zadrzyńska, On nonstationary motion of a fixed mass of a general viscous compressible heat conducting capillary fluid bounded by a free boundary

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.