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Domain sensitivity in singular limits of compressible viscous fluids

Eduard Feireisl

Séminaire Laurent Schwartz — EDP et applications

In this note, we discuss several recently developed methods for studying stability of a singular limit process with respect to the shape of the underlying physical space. As a model example, we consider a compressible viscous barotropic fluid occupying a spatial domain Ω R 3 . In what follows, we describe two rather different problems: (i) the choice of effective boundary conditions; (ii) the fluid flow in the low Mach number regime. In the remaining part of the paper, we analyze these two issues simultaneously...

On the motion of rigid bodies in a viscous fluid

Eduard Feireisl — 2002

Applications of Mathematics

We consider the problem of motion of several rigid bodies in a viscous fluid. Both compressible and incompressible fluids are studied. In both cases, the existence of globally defined weak solutions is established regardless possible collisions of two or more rigid objects.

Compensated compactness and time-periodic solutions to non-autonomous quasilinear telegraph equations

Eduard Feireisl — 1990

Aplikace matematiky

In the present paper, the existence of a weak time-periodic solution to the nonlinear telegraph equation U t t + d U t - σ ( x , t , U x ) x + a U = f ( x , t , U x , U t , U ) with the Dirichlet boundary conditions is proved. No “smallness” assumptions are made concerning the function f . The main idea of the proof relies on the compensated compactness theory.

Time-periodic solutions of a quasilinear beam equation via accelerated convergence methods

Eduard Feireisl — 1988

Aplikace matematiky

The author investigates time-periodic solutions of the quasilinear beam equation with the help of accelerated convergence methods. Using the Newton iteration scheme, the problem is approximated by a sequence of linear equations solved via the Galerkin method. The derivatiove loss inherent to this kind of problems is compensated by taking advantage of smoothing operators.

Small time-periodic solutions to a nonlinear equation of a vibrating string

Eduard Feireisl — 1987

Aplikace matematiky

In this paper, the system consisting of two nonlinear equations is studied. The former is hyperbolic with a dissipative term and the latter is elliptic. In a special case, the system reduces to the approximate model for the damped transversal vibrations of a string proposed by G. F. Carrier and R. Narasimha. Taking advantage of accelerated convergence methods, the existence of at least one time-periodic solution is stated on condition that the right-hand side of the system is sufficiently small.

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