In this paper we investigate the compressible Navier-Stokes-Cahn-Hilliard equations (the so-called NSCH model) derived by Lowengrub and Truskinowsky. This model describes the ow of a binary compressible mixture; the uids are supposed to be macroscopically immiscible, but partial mixing is permitted leading to narrow transition layers. The internal structure and macroscopic dynamics of these lay...

We study the motion of the steady compressible heat conducting viscous fluid in a bounded three dimensional domain governed by the compressible Navier-StokesFourier system. Our main result is the existence of a weak solution to these equations for arbitrarily large data. A key element of the proof is a special approximation of the original system guaranteeing pointwise uniform boundedness of th...

There exist complex behavior of the solution to 1D compressible Navier-Stokes equations in half space. We find an interesting phenomenon on isentropic with constant viscosity coefficient x , t ∈ open="[" 0 + ∞ × ...

Non reflecting boundary conditions on artificial frontiers of the domain axe proposed for both incompressible and compressible Navier-Stokes équations. For incompressible flows, the boundary conditions lead to a well-posed problem, convey properly the vortices without any reflections on the artificial limits and allow to compute turbulent flows at high Reynolds numbers. For compressible flows, ...

We study the low Mach low Freude numbers limit in the compressible Navier-Stokes equations and the transport equation for evolution of an entropy variable – the potential temperature Θ. We consider the case of well-prepared initial data on ”flat” tours and Reynolds number tending to infinity, and the case of ill-prepared data on an infinite slab. In both cases, we show that the weak solutions t...

In this paper, we study a nonlinear interaction problem between thermoelastic shell and heat-conducting fluid. The is governed by linear thermoelasticity equations encompasses time-dependent domain which filled with fluid the full Navier-Stokes-Fourier system. are fully coupled, giving rise to novel moving boundary fluid-structure involving heat exchange. existence of weak solution obtained com...

This paper is devoted to the low Mach number limit of weak solutions to the compressible Navier-Stokes equations for isentropic uids in the whole space R d (d = 2 or 3). This problem was investigated by P.L. Lions and N. Masmoudi 19]. We present here a diierent approach based upon Strichartz' estimates for the linear wave equation like in 21] in the inviscid case, which improves the convergence...