Existence and uniqueness of stationary solutions for a viscous compressible heat-conducting fluid with large potential and small nonpotential external forces

Existence and uniqueness of stationary solutions to the equations of viscous compressible heat-conductive fluid in bounded domains are well known provided the external forces and the boundary data are “sufficiently small in appropriate norms.” We show that existence and uniqueness hold also for large potential forces with “small” nonpotential perturbations. We consider the Dirichlet boundary conditions on the velocity under which there is neither outflow nor inflow.