Compressible Navier–Stokes equations with heterogeneous pressure laws

This paper concerns the existence of global weak solutions \`a la Leray for compressible Navier-Stokes equations with a pressure law that depends on density and time space variables $t$ $x$. The assumptions contain only locally Lipschitz assumption respect to variable some hypothesis extra variables. It may be seen as first step consider heat-conducting physical laws such truncated virial assumption. focuses construction approximate through new regularized fixed point procedure stability process taking advantage method introduced by two authors careful study an appropriate quantity linked pressure.