Abstract
We consider in an infinite horizontal layer the stationary convective flow of a viscous compressible and heat-conductive fluid subject to gravitational force, where the slip boundary condition for the velocity and the boundary condition of the temperature near the hydrostatic distribution are assumed. The existence of stationary solution close to hydrostatic state is obtained in Sobolev spaces as limit of fixed points of some suitable operators.
Acknowledgments
We thank the anonymous referees for various comments, specially the question on the existence of the stationary solution, which has been clarified in Remark 7.1.
Disclosure statement
No potential conflict of interest was reported by the author(s).