On stationary convective motion of viscous compressible and heat-conductive fluid

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.

Keywords:

• Existence of stationary convective motion
• viscous compressible heat-conductive fluid
• hydrostatic distribution
• slip boundary condition
• Schauder's fixed point theorem
• gravitational force

2010 Mathematics Subject Classifications:

• 76N10
• 35Q35
• 35L60
• 35L65

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).