A new construction of weak solutions to compressible Navier-Stokes equations

We prove the existence of the weak solutions to the compressible Navier–Stokes system with barotropic pressure $p(\varrho )={\varrho }^{\gamma }$ for $\gamma \ge 9\mathrm{/}5$ in three space dimension. The novelty of the paper is the approximation scheme that instead of the classical regularization of the continuity equation (based on the viscosity approximation $\text{ep}\mathrm{\Delta }\varrho$) uses more direct truncation and regularisation of nonlinear terms an the pressure. This scheme is compatible with the Bresch-Jabin compactness criterion for the density. We revisit this criterion and prove, in full rigour, that it can be applied in our approximation at any level.