Abstract
In this paper, we study strong solutions to the steady compressible heat-conductive fluid near a non-zero constant flow with the Dirichlet boundary condition for the velocity on the inflow and outflow part of the boundary. We also consider the Dirichlet boundary condition for the temperature, and we do not need the thermal conductivity coefficient κ to be large. The existence of strong solutions is established for any Reynolds number and Mach number in the framework of perturbation.
Highlights
We will study strong solutions to the steady compressible heat-conductive fluid near a non-zero constant flow in a -D finite channel = (, ) × (, )
As far as the internal friction and thermal conduction are concerned, the complete system of equations of steady compressible fluid can be expressed by div(ρu) =, ( . )
In [, ], without the smallness assumption of the Reynolds number and the Mach number, the authors can obtain the strong solutions to both isentropic fluids and heatconductive fluids under inhomogeneous slip boundary conditions when friction coefficient is large on the boundary
Summary
In [ , ], without the smallness assumption of the Reynolds number and the Mach number, the authors can obtain the strong solutions to both isentropic fluids and heatconductive fluids under inhomogeneous slip boundary conditions when friction coefficient is large on the boundary. The authors in [ ] obtained the existence of strong solutions to steady compressible isentropic fluids near a uniform non-zero constant flow in a -D channel under the Dirichlet boundary condition for the velocity on the inflow and outflow part of the boundary without the smallness assumption of both Reynolds number and the Mach number. We will take into consideration thermal conduction and study strong solutions near a non-zero constant flow with the Dirichlet boundary condition for the velocity on the inflow and outflow part of the boundary.
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