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Large data existence result for unsteady flows of inhomogeneous shear-thickening heat-conducting incompressible fluids. (English) Zbl 1213.35348
The authors study unsteady flows of inhomogeneous, incompressible, shear-thickening and heat-conducting fluids where the viscosity depends on the shear rate, density and temperature, and the heat conductivity depends on density and temperature. For large data they establish the existence of weak solutions to internal flows inside arbirary bounded domains with Lipschitz boundaries. The main novelty of the paper consists in including the changes due to heat conduction into the model.

MSC:
35Q35 PDEs in connection with fluid mechanics
35D30 Weak solutions to PDEs
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
80A20 Heat and mass transfer, heat flow (MSC2010)
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