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On local existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion

Piotr Mucha, Wojciech Zajączkowski (2000)

Applicationes Mathematicae

The local-in-time existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion is proved. We show the existence of solutions with lowest possible regularity for this problem such that u ∈ W r 2 , 1 ( Ω ˜ T ) with r>3. The existence is proved by the method of successive approximations where the solvability of the Cauchy-Neumann problem for the Stokes system is applied. We have to underline that in the L p -approach the Lagrangian coordinates must be used. We are looking...

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

W. Zajączkowski (1992)

Banach Center Publications

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....

On local-in-time existence for the Dirichlet problem for equations of compressible viscous fluids

Piotr Boguslaw Mucha, Wojciech Zajączkowski (2002)

Annales Polonici Mathematici

The local existence of solutions for the compressible Navier-Stokes equations with the Dirichlet boundary conditions in the L p -framework is proved. Next an almost-global-in-time existence of small solutions is shown. The considerations are made in Lagrangian coordinates. The result is sharp in the L p -approach, because the velocity belongs to W r 2 , 1 with r > 3.

On nonstationary motion of a fixed mass of a general fluid bounded by a free surface

Ewa Zadrzyńska, Wojciech M. Zajączkowski (2003)

Banach Center Publications

In the paper the motion of a fixed mass of a viscous compressible heat conducting fluid is considered. Assuming that the initial data are sufficiently close to an equilibrium state and the external force, the heat sources and the heat flow through the boundary vanish, we prove the existence of a global in time solution which is close to the equilibrium state for any moment of time.

On nonstationary motion of a fixed mass of a general viscous compressible heat conducting capillary fluid bounded by a free boundary

Ewa Zadrzyńska (1999)

Applicationes Mathematicae

The motion of a fixed mass of a viscous compressible heat conducting capillary fluid is examined. Assuming that the initial data are sufficiently close to a constant state and the external force vanishes we prove the existence of a global-in-time solution which is close to the constant state for any moment of time. Moreover, we present an analogous result for the case of a barotropic viscous compressible fluid.

Currently displaying 141 – 160 of 508