## Steady-state buoyancy-driven viscous flow with measure data.(English)Zbl 0981.35054

Summary: A steady-state system of equations for incompressible, possibly non-Newtonean fluids of the $$p$$-power is studied. 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 $$n=3$$).

### MSC:

 35Q35 PDEs in connection with fluid mechanics 76A05 Non-Newtonian fluids 35J60 Nonlinear elliptic equations 80A20 Heat and mass transfer, heat flow (MSC2010)
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