A stable and conservative high order multi-block method for the time-dependent compressible Navier-Stokes equations has been developed. Stability and conservation are proved using summation-by-parts operators, weak interface conditions and the energy method. This development makes it possible to exploit the efficiency of the high order finite difference method for non-trivial geometries. The co...

This paper is concerned with the construction of global, non-vacuum solutions with large amplitude to the initial-boundary value problems of the one-dimensional compressible Navier-Stokes equations with degenerate transport coefficients. The main ingredient of the analysis is to derive the positive lower and upper bounds on the specific volume and the absolute temperature.

We prove the solution of the Navier-Stokes equations for one-dimensional compressible heat-conducting fluids with centered rarefaction data of small strength exists globally in time, and moreover, as the viscosity and heat-conductivity coefficients tend to zero, the global solution converges to the centered rarefaction wave solution of the corresponding Euler equations uniformly away from the i...

We develop a dynamical systems theory for the compressible Navier-Stokes equations based on global in time weak solutions. The following questions will be addressed: • Global existence and critical values of the adiabatic constant; • dissipativity in the sense of Levinson bounded absorbing sets; • asymptotic compactness; • the long-time behaviour and attractors. 2000 Mathematics Subject Classif...

We describe in this paper a strategy for parallelising a 3D compressible Navier-Stokes solver using unstructured meshes on a class of message-passing MIMD machines. The performance results obtained on two parallel machines, the Meiko Concerto and Intel iPSC860 are presented and compared to those obtained on CRAY.

We prove the global existence of weak solutions for the 2-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient (λ = λ(ρ)). Initial data and solutions are small in energy-norm with nonnegative densities having arbitrarily large sup-norm. Then, we show that if there is a vacuum domain at the initial time, then the vacuum domain will retain for all time, and vanish...

This paper is dedicated to the construction of global weak solutions to the quantum Navier-Stokes equation, for any initial value with bounded energy and entropy. The construction is uniform with respect to the Planck constant. This allows to perform the semi-classical limit to the associated compressible Navier-Stokes equation. One of the difficulty of the problem is to deal with the degenerat...

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.

We present a technique that allows to obtain certain results in the compressible fluid theory: in particular, it is a nonexistence result for the highly decreasing at infinity solutions to the Navier-Stokes equations, the construction of the solutions with uniform deformation and the study of behavior of the boundary of a material volume of liquid.

We prove the global existence and uniqueness of strong solutions for a compressible multifluid described by the barotropic Navier-Stokes equations in dim = 1. The result holds when the diffusion coefficient depends on the pressure. It relies on a global control in time of the L norm of the space derivative of the density, via a new kind of entropy. §