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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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