Tomas Roubicek, Mathematical Institute, Charles University, Sokolovska 83, CZ-186 75 Praha 8, e-mail: roubicek@karlin.mff.cuni.cz, and Institute of Information Theory and Automation, Academy of Sciences, Pod vodarenskou vezi 4, CZ-182 08 Praha 8, Czech Republic
Abstract: 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 $\Omega\subset\R^n$, $n=2$ 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 $n=3$).
Keywords: non-Newtonean fluids, heat equation, dissipative heat, adiabatic heat
Classification (MSC 2000): 35J60, 35Q35, 76A05, 80A20
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