On non-Newtonian fluids with convective effects

Abstract

We study a system of partial differential equations describing a steady thermoconvective flow of a non-Newtonian fluid. We assume that the stress tensor and the heat flux depend on temperature and satisfy the conditions of p,q-coercivity with $p>\frac{2n}{n+2}$, $q>\frac{np}{p(n+1)-n}$, respectively. Considering Dirichlet boundary conditions for the velocity and a mixed and nonlinear boundary condition for the temperature, we prove the existence of weak solutions. We also analyze the existence and uniqueness of strong solutions for small and suitably regular data.

Keywords

• Non-Newtonian fluids
• shear-dependent viscosity
• weak solutions
• strong solutions
• uniqueness