We consider the initial value problem for multi-dimensional bipolar compressible Navier– Stokes–Poisson equations, and show the global existence and uniqueness of the strong solution in hybrid Besov spaces with the initial data close to an equilibrium state.

For the numerical resolution of the compressible Navier-Stokes equations (NS) with Finite Volumes (FV) two main approaches have called the attention of researchers and engineers. First, following the hyperbolic nature of the compressible NS equations, the Godunov-like schemes discretize the numerical fluxes by a characteristic analysis. Second, disregarding the hyperbolicity of the equations, t...

This contribution is devoted to the mathematical modelling of a compressible viscous fluid flow through a 2-D model of the male rotor-housing gap in screw machines. Numerical solution of the nonlinear conservative system of the compressible Navier-Stokes equations is obtained by means of the cell-centred finite volume formulation of the explicit two-step TVD MacCormack scheme proposed by Causon...

We look at adaptive time integration in the context of discontinuous Galerkin methods for the three dimensional unsteady compressible Navier-Stokes equations. Several explicit and implicit schemes will be compared. Philipp Birken, Gregor Gassner, Mark Haas and Claus-Dieter Munz

We consider the Navier–Stokes equations for compressible isothermal flow in the steady two dimensional case and show the existence of a weak solution in the case of periodic and of mixed boundary conditions.

In the paper compressible, stationary Navier-Stokes equations are considered. A framework for analysis of such equations is established. In particular, the well-posedness for inhomogeneous boundary value problems of elliptic-hyperbolic type is shown. Analysis is performed for small perturbations of the so-called approximate solutions, i.e., the solutions take form (1.12). The approximate soluti...

In [3, 4, 5], we have developed a new tool called tquasi solutions which approximate in some sense the compressible Navier-Stokes equation. In particular it allows to obtain global strong solution for the compressible Navier-Stokes equations with large initial data on the irrotational part of the velocity (large in the sense that the smallness assumption is subcritical in terms of scaling, it t...

In this paper, we study the convergence of weak and strong solutions of oscillatory perturbations of the Navier-Stokes equations and in particular the asymptotic behaviour of rotating uids and of slightly compressible uids.

In this paper we prove the nonexistence of global weak solutions to the compressible Navier-Stokes equations for the isentropic gas in R N , N ≥ 3, where the pressure law given by p(ρ) = aρ γ , a > 0, 1 < γ ≤