Steady-state buoyancy-driven viscous flow with measure data

summary:Steady-state system of equations for incompressible, possibly non-Newtonean of the $p$-power type, viscous flow coupled with the heat equation is considered in a smooth bounded domain $\Omega \subset \mathbb{R}^n$, $n=2$ or 3, with heat sources allowed to have a natural $L^1$-structure and even to be measures. The existence of a distributional solution is shown by a fixed-point technique for sufficiently small data if $p>3/2$ (for $n=2$) or if $p>9/5$ (for $n=3$)