Wyniki wyszukiwania

1

On global motion of a compressible barotropic viscous fluid with boundary slip condition

100%

Kobayashi T., Zajączkowski W. M.

Applicationes Mathematicae

|

1999

|

tom 26

|

nr 2

159-194

EN

Global-in-time existence of solutions for equations of viscous compressible barotropic fluid in a bounded domain Ω ⊂ $ℝ^3$ with the boundary slip condition is proved. The solution is close to an equilibrium solution. The proof is based on the energy method. Moreover, in the $L_2$-approach the result is sharp (the regularity of the solution cannot be decreased) because the velocity belongs to $H^{2+α,1+α/2}(Ω × ℝ_+)$ and the density belongs to $H^{1+α,1/2+α/2}(Ω× ℝ_+)$, α ∈ (1/2,1).

2

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

89%

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

3

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

88%

Zajączkowski W. M.

Banach Center Publications

|

1992

|

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.

Ograniczanie wyników

1 Applicationes Mathematicae

1 Banach Center Publications

3 Zajączkowski W. M.

1 Kobayashi T.

1 1999

1 1993

1 1992

On global motion of a compressible barotropic viscous fluid with boundary slip condition

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

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