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3 Journal of Applied Analysis

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

100%

Zajączkowski W. M.

1998

tom Vol. 4, nr 2

167-204

Global existence of solutions of equations of compressible barotropic viscous fluids in a bounded domain with boundary slip condition which are sufficiently close to a rest state is proved. Moreover, stability of the solutions and existence of corresponding stationary solutions are shown too.

Existence of solutions and L∞ - boundsfor quasilinear degenerate parabolic systems

63%

Wrzosek D. , Zajączkowski W. M.

1999

tom Vol. 5, nr 2

197-221

Existence of weak solutions for systems of quasilinear degenerate parabolic equations with non-diagonal main part and nonlinear boundary conditions is proved. Under some restrictions we find also L∞ - bounds for the solutions.

Local existence of solutions of a free boundary problem for equations of compressible viscous heat-conducting capillary fluids

63%

Zadrzyńska E. , Zajączkowski W. M.

2000

tom Vol. 6, nr 2

227-250

In the paper the motion of a viscous compressible heat conducting capillary fluid in a domain bounded by a free surface is considered. We prove the local existence and uniqueness of a solution to a problem describing such a motion in anisotropic Sobolev-Slobodetskii spaces. This solution is such that the velocity and temperature belong to (wzór), and density to (wzór).