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Noncharacteristic mixed problems for hyperbolic systems of the first order

Ewa Zadrzyńska — 1991

CONTENTS1. Introduction....................................................................................................................................................52. Notations and preliminaries .........................................................................................................................11 2.1. Function spaces and spaces of distributions............................................................................................11 2.2. Perturbations of linear operators.............................................................................................................20 2.3....

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.

On some free boundary problems for Navier-Stokes equations

Ewa Zadrzyńska — 2005

Banach Center Publications

In this survey we report on existence results for some free boundary problems for equations describing motions of both incompressible and compressible viscous fluids. We also present ways of controlling free boundaries in two cases: a) when the free boundary is governed by surface tension, b) when surface tension does not occur.

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

Ewa ZadrzyńskaWojciech Zajączkowski — 1998

Applicationes Mathematicae

The local existence and the uniqueness of solutions for equations describing the motion of viscous compressible heat-conducting fluids in a domain bounded by a free surface is proved. First, we prove the existence of solutions of some auxiliary problems by the Galerkin method and by regularization techniques. Next, we use the method of successive approximations to prove the local existence for the main problem.

On the global existence theorem for a free boundary problem for equations of a viscous compressible heat conducting fluid

Ewa ZadrzyńskaWojciech M. Zajączkowski — 1996

Annales Polonici Mathematici

We consider the motion of a viscous compressible heat conducting fluid in ℝ³ bounded by a free surface which is under constant exterior pressure. Assuming that the initial velocity is sufficiently small, the initial density and the initial temperature are close to constants, the external force, the heat sources and the heat flow vanish, we prove the existence of global-in-time solutions which satisfy, at any moment of time, the properties prescribed at the initial moment.

On some inequalities for solutions of equations describing the motion of a viscous compressible heat-conducting capillary fluid bounded by a free surface

Ewa ZadrzyńskaWojciech M. Zajączkowski — 2001

Applicationes Mathematicae

We derive inequalities for a local solution of a free boundary problem for a viscous compressible heat-conducting capillary fluid. The inequalities are crucial in proving the global existence of solutions belonging to certain anisotropic Sobolev-Slobodetskii space and close to an equilibrium state.

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

Ewa ZadrzyńskaWojciech 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.

Some linear parabolic system in Besov spaces

Ewa ZadrzyńskaWojciech M. Zajączkowski — 2008

Banach Center Publications

We study the solvability in anisotropic Besov spaces B p , q σ / 2 , σ ( Ω T ) , σ ∈ ℝ₊, p,q ∈ (1,∞) of an initial-boundary value problem for the linear parabolic system which arises in the study of the compressible Navier-Stokes system with boundary slip conditions. The proof of existence of a unique solution in B p , q σ / 2 + 1 , σ + 2 ( Ω T ) is divided into three steps: 1° First the existence of solutions to the problem with vanishing initial conditions is proved by applying the Paley-Littlewood decomposition and some ideas of Triebel. All considerations...

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