About the barotropic compressible quantum Navier–Stokes equations

About the barotropic compressible quantum Navier-Stokes equations

On the barotropic compressible Navier-Stokes equations

We consider barotropic compressible Navier-Stokes equations with density dependent viscosity coefficients that vanish on vacuum. We prove the stability of weak solutions in periodic domain Ω = T and in the whole space Ω = R , when N = 2 and N = 3. The pressure is given by p(ρ) = ρ and our result holds for any γ > 1. Note that our notion of weak solutions is not the usual one. In particular we r...

The Dynamical Systems Approach to the Equations of a Linearly Viscous Compressible Barotropic Fluid

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...

Beltrami States for Compressible Barotropic Flows

Beltrami states for compressible barotropic flows are deduced by minimizing the total kinetic energy while keeping the total helicity constant. A Hamiltonian basis for these Beltrami states is also sketched.

Regularity of weak solutions of the compressible barotropic Navier-Stokes equations

Regularity and uniqueness of weak solutions of the compressible barotropic NavierStokes equations with constant viscosity coefficients is proven for small time in dimension N = 2, 3 under periodic boundary conditions. In this paper, the initial density is not required to have a positive lower bound and the pressure law is assumed to satisfy a condition that reduces to P (ρ) = aρ with γ > 1 (in ...