Existence of weak solutions to the three-dimensional steady compressible Navier–Stokes equations for any specific heat ratio $\gamma>1$

Abstract

In this paper we present the recent existence results from [14], [15] on weak solutions to the the steady Navier–Stokes equations for three-dimensional compressible isentropic flows with large data for any specific heat ratio $\gamma \gt 1$. The existence is proved in the framework of the weak convergence method due to Lions [16] by establishing a new a priori potential estimate of both pressure and kinetic energy (in a Morrey space) and using a bootstrap argument. The results presented in the current paper extend the existence of weak solutions in [9] from $\gamma \gt 4/3$ to $\gamma \gt 1$.