New regularity estimates for compressible Navier-Stokes

We present a new approach offering explicit regularity estimates for solutions to transport equations, and in particular for the density of the solutions to the compressible Navier-Stokes equations. This new method removes several constraints of the classical Lions-Feireisl theory. It thus allows us to treat a larger class of models with *non* *monotone* *pressure* terms, or *anisotropic* *viscosity* for instance, leading to many applications from geophysical flows (eddy viscosity) to solar events (virial pressure law) and some biological situations.