We consider relativistic and ”semi-relativistic” models of radiative viscous compressible Navier-Stokes-Fourier system coupled to the radiative transfer equation extending the classical model introduced in [1] and we study some of its singular limits (low Mach and diffusion) in the case of well-prepared initial data and Dirichlet boundary condition for the velocity field. In the low Mach number...

On compactness of solutions to the compressible isentropic Navier-Stokes equations when the density is not square integrable Abstract. We show compactness of bounded sets of weak solutions to the isentropic compressible Navier-Stokes equations in three space dimensions under the hypothesis that the adiabatic constant γ > 3/2.

For the purpose of engineering, it is important to study convergent rates in process low Mach number limit. However, there are only a few results on this issue, which focus cases isentropic regime or ones without solid boundaries. In paper, we obtain convergence for local strong solutions non-isentropic compressible Navier-Stokes equations with well-prepared initial data and Navier-slip boundar...

Visualizations of Rayleigh–Taylor turbulent mixing layers are presented. Three Navier–Stokes models are used: Boussinesq, anelastic and fully compressible. Isosurfaces and slices of concentration, vorticity, Q-criterion, turbulent kinetic energy, local Taylor-microscale Reynolds number, dissipation, pressure and temperature are displayed. This gives an overall picture of the Rayleigh–Taylor flo...

In this paper, based on the BGK equation, Liouville's theorem, and symplecticity preserving property of a Hamiltonian flow, a well-balanced kinetic scheme for the compressible Navier-Stokes equations under external forcing field is developed. In order to construct such a scheme, the physical process of particles transport through a potential barrier at a cell interface will be modeled with pene...

The quasineutral limit of compressible Navier-Stokes-Poisson system with heat conductivity and general (ill-prepared) initial data is rigorously proved in this paper. It is proved that, as the Debye length tends to zero, the solution of the compressible Navier-Stokes-Poisson system converges strongly to the strong solution of the incompressible Navier-Stokes equations plus a term of fast singul...

It is shown that expansion waves for the compressible Navier-Stokes equations are nonlinearly stable. The expansion waves are constructed for the compressible Euler equations based on the inviscid Burgers equation. Our result shows that Navier-Stokes equations and Euler equations are timeasymptotically equivalent on the level of expansion waves. The result is proved using the energy method, mak...

We consider a multidimensional model for the dynamic combustion of compressible reacting fluids formulated by the Navier Stokes equations in Euler coordinates. For the chemical model we consider a one way irreversible chemical reaction governed by the Arrhenius kinetics. The existence of globally defined weak solutions of the Navier-Stokes equations for compressible reacting fluids is establish...

We investigate the self-similar solutions to the isothermal compressible Navier–Stokes equations. The aim of this paper is to show that there exist neither forward nor backward self-similar solutions with finite total energy. This generalizes the results for the incompressible case in Nečas, J., Ru̇žička, M. & Šverák, V. (1996, On Leray’s self-similar solutions of the Navier-Stokes equations. Ac...