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On an initial-boundary value problem for the parabolic system which appears in free boundary problems for compressible Navier-Stokes equations

100%

Zajączkowski W. M.

Instytut Matematyczny Polskiej Akademii Nauk

EN

CONTENTS 1. Introduction................................................................5 2. Problem (1-1) in a half-space.....................................7 3. A priori estimate and existence of solutions of problem (1.1) with vanishing initial conditions............................20 4. Existence of solutions of problem (1.1)....................28 References..................................................................33

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On local motion of a compressible barotropic viscous fluid bounded by a free surface

96%

Zajączkowski W. M.

Banach Center Publications

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1992

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tom 27

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

61%

Ströhmer G., Zajączkowski W. M.

Applicationes Mathematicae

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1999

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tom 26

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nr 1

1-31

EN

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.

Ograniczanie wyników

1 Applicationes Mathematicae

1 Banach Center Publications

3 Zajączkowski W. M.

1 Ströhmer G.

1 1999

1 1992

1 1990

On an initial-boundary value problem for the parabolic system which appears in free boundary problems for compressible Navier-Stokes equations

On local motion of a compressible barotropic viscous fluid bounded by a free surface

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