It is conjectured that Darcy’s law governs the motion of compressible porous media flow in large time. This has been justified for one-dimensional isentropic flows. In this work, we show the conjecture is true for one-dimensional adiabatic flows with generic small smooth initial data. © 2004 Elsevier Inc. All rights reserved.

A stability result for the compressible Navier-Stokes system with transport equation for entropy s is shown. The proof comes as an outcome of the isentropic case and additional properties of the effective viscous flux. We deal with the pressure term in the form ρ γ e s with adiabatic index γ > 3/2; therefore the crucial renormalization method is restricted.

In this paper we study the self-propelled motion of a single deformable body in a viscous compressible fluid which occupies whole 3-dimensional Euclidean space. The considered governing system for the fluid is the isentropic compressible Navier-Stokes equations. The main result of this paper is the existence of a weak solution on a time interval (0,+∞).

The dynamics of gaseous stars can be described by the EulerPoisson system. Inspired by Rein’s stability result for γ > 4 3 , we prove the nonlinear instability of steady states for the adiabatic exponent γ = 6 5 in spherically symmetric and isentropic motion.

In this paper, we investigate the characteristic structure of the full equations of magnetohydrodynamics (MHD) and show that it satisfies the hypotheses of a general variable-multiplicity stability framework introduced by Métivier and Zumbrun, thereby extending to the general case various results obtained by Métivier and Zumbrun for the isentropic equations of MHD.

Convergence of a second-order shock-capturing scheme for the system of isentropic gas dynamics with L°° initial data is established by analyzing the entropy dissipation measures. This scheme is modified from the classical MUSCL scheme to treat the vacuum problem in gas fluids and to capture local entropy near shock waves. Convergence of this scheme for the piston problem is also discussed.

This paper represents a technique for finding optimal paths with multiple indexes in a graph. Up to the present time, all optimal paths have been determined upon one index, say, distance for which an evaluation method exists. In this paper firstly we define multiple indexes for each edge in such a way that anyone can treat the factor for assigning an optimal path. Here, we use Data Envelopment ...

The three-dimensional equations of compressible magnetohydrodynamic isentropic flows are considered. An initial-boundary value problem is studied in a bounded domain with large data. The existence and large-time behavior of global weak solutions are established through a three-level approximation, energy estimates, and weak convergence for the adiabatic exponent γ > 3 2 and constant viscosity c...

Abstract The Cauchy problem for the three-dimensional Euler–Boltzmann equations of a polytropic, ideal and isentropic fluid in radiation hydrodynamics is considered. The formation of singularities in smooth solutions is studied. It is proved that some C1 solutions, regardless of the size of the initial disturbance, will develop singularities in a finite time provided that the initial disturbanc...

In this paper we consider the non-isentropic equations of gas dynamics with the entropy preserved. Equations are formulated so that the problem is reduced into the 2 2 system of conservation laws with a forcing term in momentum equation. The method of compensated compactness is then applied to prove the existence of weak solution in the vanishing viscosity method.