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Asymptotic behavior of the solutions to a one-dimensional motion of compressible viscous fluids

Shigenori Yanagi (1995)

Mathematica Bohemica

We study the one-dimensional motion of the viscous gas represented by the system v t - u x = 0 , u t + p ( v ) x = μ ( u x / v ) x + f 0 x v x ¨ , t , with the initial and the boundary conditions ( v ( x , 0 ) , u ( x , 0 ) ) = ( v 0 ( x ) , u 0 ( x ) ) , u ( 0 , t ) = u ( X , t ) = 0 . We are concerned with the external forces, namely the function f , which do not become small for large time t . The main purpose is to show how the solution to this problem behaves around the stationary one, and the proof is based on an elementary L 2 -energy method.

Bipolar Barotropic Non-Newtonian Compressible Fluids

Šárka Matušu-Nečasová, Mária Medviďová-Lukáčová (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We are interested in a barotropic motion of the non-Newtonian bipolar fluids . We consider a special case where the stress tensor is expressed in the form of potentials depending on eii and ( e i j x k ) . We prove the asymptotic stability of the rest state under the assumption of the regularity of the potential forces.

Description of the multi-dimensional finite volume solver EULER

Pavel Šolín, Karel Segeth (2002)

Applications of Mathematics

This paper is aimed at the description of the multi-dimensional finite volume solver EULER, which has been developed for the numerical solution of the compressible Euler equations during several last years. The present overview of numerical schemes and the explanation of numerical techniques and tricks which have been used for EULER could be of certain interest not only for registered users but also for numerical mathematicians who have decided to implement a finite volume solver themselves. This...

Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions

David Hoff (2001)

Journées équations aux dérivées partielles

We prove the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these discontinuities are shown to decay exponentially in time, more rapidly for larger acoustic speeds and smaller...

Equations of magnetohydrodynamics of compressible fluid: Periodic solutions

Milan Štědrý, Otto Vejvoda (1985)

Aplikace matematiky

The authors prove the global existence and exponential stability of solutions of the given system of equations under the condition that the initial velocities and the external forces are small and the initial density is not far from a constant one. If the external forces are periodic, then solutions periodic with the same period are obtained. The investigated system of equations is a bit non-standard - for example the displacement current in the Maxwell equations is not neglected.

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