# On local motion of a general compressible viscous heat conducting fluid bounded by a free surface

Ewa Zadrzyńska; Wojciech M. Zajączkowski

Annales Polonici Mathematici (1994)

- Volume: 59, Issue: 2, page 133-170
- ISSN: 0066-2216

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topEwa Zadrzyńska, and Wojciech M. Zajączkowski. "On local motion of a general compressible viscous heat conducting fluid bounded by a free surface." Annales Polonici Mathematici 59.2 (1994): 133-170. <http://eudml.org/doc/262367>.

@article{EwaZadrzyńska1994,

abstract = {The motion of a viscous compressible heat conducting fluid in a domain in ℝ³ bounded by a free surface is considered. We prove local existence and uniqueness of solutions in Sobolev-Slobodetskiĭ spaces in two cases: with surface tension and without it.},

author = {Ewa Zadrzyńska, Wojciech M. Zajączkowski},

journal = {Annales Polonici Mathematici},

keywords = {free boundary; compressible viscuous heat conducting fluid; local existence; anisotropic Sobolev spaces; compressible heat conducting fluid},

language = {eng},

number = {2},

pages = {133-170},

title = {On local motion of a general compressible viscous heat conducting fluid bounded by a free surface},

url = {http://eudml.org/doc/262367},

volume = {59},

year = {1994},

}

TY - JOUR

AU - Ewa Zadrzyńska

AU - Wojciech M. Zajączkowski

TI - On local motion of a general compressible viscous heat conducting fluid bounded by a free surface

JO - Annales Polonici Mathematici

PY - 1994

VL - 59

IS - 2

SP - 133

EP - 170

AB - The motion of a viscous compressible heat conducting fluid in a domain in ℝ³ bounded by a free surface is considered. We prove local existence and uniqueness of solutions in Sobolev-Slobodetskiĭ spaces in two cases: with surface tension and without it.

LA - eng

KW - free boundary; compressible viscuous heat conducting fluid; local existence; anisotropic Sobolev spaces; compressible heat conducting fluid

UR - http://eudml.org/doc/262367

ER -

## References

top- [1] R. A. Adams, Sobolev Spaces, Academic Press, 1975.
- [2] G. Allain, Small-time existence for the Navier-Stokes equations with a free surface, Appl. Math. Optim. 16 (1987), 37-50.
- [3] O. V. Besov, V. P. Il'in and S. M. Nikol'skiĭ, Integral Representations of Functions and Imbedding Theorems, Nauka, Moscow, 1975 (in Russian).
- [4] L. Landau and E. Lifschitz, Hydrodynamics, Nauka, Moscow, 1986 (in Russian).
- [5] T. Nishida, Equations of fluid dynamics: free surface problems, Comm. Pure Appl. Math. 39 (1986), 221-238.
- [6] P. Secchi and A. Valli, A free boundary problem for compressible viscous fluids, J. Reine Angew. Math. 341 (1983), 1-31. Zbl0502.76082
- [7] V. A. Solonnikov, A priori estimates for parabolic equations of second order, Trudy Mat. Inst. Steklov. 70 (1964), 133-212 (in Russian).
- [8] V. A. Solonnikov, On boundary problems for linear parabolic systems of differential equations of general type, Trudy Mat. Inst. Steklov. 83 (1965) (in Russian); English transl.: Proc. Steklov Inst. Math. 83 (1967). Zbl0164.12502
- [9] V. A. Solonnikov, On the solvability of the initial-boundary value problem for equations of motion of the viscous compressible fluid, Zap. Nauchn. Sem. LOMI 56 (1976), 128-142 (in Russian). Zbl0338.35078
- [10] V. A. Solonnikov, On an unsteady motion of an isolated volume of a viscous incompressible fluid, Izv. Akad. Nauk SSSR Ser. Mat. 51 (5) (1987), 1065-1087 (in Russian).
- [11] 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).
- [12] V. Solonnikov and A. Tani, Free boundary problem for a viscous compressible flow with surface tension, in: Constantine Carathéodory: An International Tribute, T. M. Rassias (ed.), World Scientific, 1991, 1270-1303. Zbl0752.35096
- [13] W. M. Zajączkowski, On local motion of a compressible barotropic viscous fluid bounded by a free surface, in: Partial Differential Equations, Banach Center Publ. 27, Inst. Math., Polish Acad. Sci., Warszawa, 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, to appear. Zbl0813.35086
- [16] W. M. Zajączkowski, Local existence of solutions for free boundary problems for viscous fluids, to appear.

## Citations in EuDML Documents

top- Ewa Zadrzyńska, Wojciech Zajączkowski, Local existence of solutions of a free boundary problem for equations of compressible viscous heat-conducting fluids
- W. M. Zajączkowski, Existence of local solutions for free boundary problems for viscous compressible barotropic fluids
- Ewa Zadrzyńska, Wojciech M. Zajączkowski, On a differential inequality for a viscous compressible heat conducting capillary fluid bounded by a free surface
- 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
- Alfred Wagner, Nonstationary Marangoni convection
- 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

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