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

W. M. Zajączkowski

Annales Polonici Mathematici (1995)

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

Abstract

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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].

How to cite

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W. 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

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  1. [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. [2] D. K. Faddeev, V. A. Solonnikov and N. N. Ural'tseva, Selected Topics of Analysis and Algebra, Leningrad, 1981 (in Russian). 
  3. [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. [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. [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. [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. [7] V. A. Solonnikov, A priori estimates for second order parabolic equations, ibid. 70 (1964), 133-212 (in Russian). Zbl0168.08202
  8. [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. [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. [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. [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. [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. [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. [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. [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

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

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