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

100%
Zadrzyńska E., Zajączkowski W.
Annales Polonici Mathematici
|
1994
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tom 59
|
nr 2
133-170
EN
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.
2
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Existence of local solutions for free boundary problems for viscous compressible barotropic fluids

100%
Zajączkowski W.
Annales Polonici Mathematici
|
1994-1995
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tom 60
|
nr 3
255-287
EN
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].
3
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On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface

90%
Zajączkowski W. M.
Instytut Matematyczny Polskiej Akademii Nauk
EN
We consider the motion of a viscous compressible barotropic fluid in $ℝ^3$ bounded by a free surface which is under constant exterior pressure. For a given initial density, initial domain and initial velocity we prove the existence of local-in-time highly regular solutions. Next assuming that the initial density is sufficiently close to a constant, the initial pressure is sufficiently close to the external pressure, the initial velocity is sufficiently small and the external force vanishes we prove the existence of global-in-time solutions which satisfy, at any moment of time, the properties prescribed at the initial moment.
XX
CONTENTS 1. Introduction.......................................5 2. Global estimates and relations........11 3. Local existence...............................16 4. Global differential inequality............44 5. Korn inequality................................81 6. Global existence.............................89 References.......................................100
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Entropy solution for doubly nonlinear elliptic anisotropic problems with Fourier boundary conditions

88%
Ibrango I., Ouaro S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2015
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tom 35
|
nr 2
123-150
EN
The goal of this paper is to study nonlinear anisotropic problems with Fourier boundary conditions. We first prove, by using the technic of monotone operators in Banach spaces, the existence of weak solutions, and by approximation methods, we prove a result of existence and uniqueness of entropy solution.
5
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On local motion of a compressible barotropic viscous fluid bounded by a free surface

88%
Zajączkowski W. M.
Banach Center Publications
|
1992
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tom 27
|
nr 2
511-553
EN
We consider the motion of a viscous compressible barotropic fluid in ℝ³ bounded by a free surface which is under constant exterior pressure, both with surface tension and without it. In the first case we prove local existence of solutions in anisotropic Hilbert spaces with noninteger derivatives. In the case without surface tension the anisotropic Sobolev spaces with integration exponent p > 3 are used to omit the coefficients which are increasing functions of 1/T, where T is the existence time.
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