On the existence of weak solutions to the equations of steady flow of heat-conducting fluids with dissipative heating

Abstract

We study a system of partial differential equations describing the steady flow of a heat conducting incompressible fluid in a bounded three dimensional domain, where the right-hand side of the momentum equation includes the buoyancy force. In the present work we prove the existence of a weak solution under both the smallness and a sign condition on physical parameters alpha(0) and alpha(1) which appear on the right hand side.

Keywords

• Heat conducting Newtonian fluid
• Buoyancy force
• Steady problem
• Weak solution
• Reverse Holder inequality