On the existence of weak solutions to the steady compressible Navier-Stokes equations when the density is not square integrable

Abstract

We consider the steady compressible Navier-Stokes equations in the isentropic regime in a bounded domain of $\mathbb{R}^{3}$. We show that the renormalized continuity equation holds even if the density is not square integrable. We use this result to prove existence of weak solutions under the sole hypothesis $\gamma > 3/2$ for the adiabatic constant.