The talk aims at the existence issue for the weak solutions to the compressible Navier--Stokes system with barotropic pressure $p(\rho) \sim \rho^\gamma$ for $\gamma \geq 9/5$ 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 $\varepsilon \Delta \varrho$) 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.
Based on the joint paper with N Chaudhuri and E Zatorska: arXiv:2211.12189
