Existence of Solutions of Stationary Compressible Navier–Stokes Equations with Large Force

In this paper, we consider the Navier–Stokes equations for isentropic, compressible flows of a polytropic gas in a bounded domain. The equations to be considered are obtained by scaling to dimensionless form and then replacing the density ρ by ρ+ε2ρ, where ε is a Mach number. The existence of solutions has been known only for small forces or large potential forces near a rest state. The aim of this paper is to give a proof of the existence of stationary compressible Navier–Stokes equations with large force, when the Mach number ε is small.