Existence of radially symmetric stationary solutions for viscous and Heat-conductive ideal Gas

We consider the existence of radially symmetric stationary solutions of the compressible viscous and heat-conductive polytropic ideal fluid on the unbounded exterior domain of a sphere where the boundary and far-field conditions are prescribed. The unique existence of the stationary solution is shown for both inflow and outflow problems in a suitably small neighborhood of the far-field state. Estimates of the algebraic decay rate toward the far field state are also obtained.