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Stationary solutions to a quasi-Newtonian flow with viscous heating. (English) Zbl 0838.76003

Summary: System of equations describing the stationary flow of a quasi-Newtonian fluid, with temperature-dependent viscosity and with a viscous heating, is considered. Existence of at least one appropriate weak solution is proved, i.e. we get existence of at least one velocity field having finite energy and existence of a nonnegative temperature field. Its regularity is a consequence of the \(L^1\)-forcing term generated by the viscous heating.

MSC:

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