Global existence of weak solutions for Navier-Stokes Equations with thermodynamically unstable pressure and anisotropic viscous stress
We provide global existence of weak solutions for the compressible
Navier-Stokes equations for more general stress tensor than those
covered by P.-L. Lions and E. Feireisl's theory. More
precisely we focus on more general pressure laws which are not
thermodynamically stable and on anisotropy in the viscous stress tensor.
Considering these two cases is important in practical situations for
instance to describe solar events (virial pressure law), geophysical
flows (eddy viscosity) or biological situations (anisotropy).