MATHEMATICA BOHEMICA, Vol. 126, No. 2, pp. 493-504 (2001)

Steady-state buoyancy-driven viscous flow with measure data

Tomas Roubicek

Tomas Roubicek, Mathematical Institute, Charles University, Sokolovska 83, CZ-186 75 Praha 8, e-mail:, 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 (MSC2000): 35J60, 35Q35, 76A05, 80A20

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