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On the motion of shear-thinning heat-conducting incompressible fluid-rigid system. (English) Zbl 1403.35202

Summary: The full Navier-Stokes-Fourier system with mixed boundary condition that describes the motion of shear-thinning and incompressible viscous fluid in a rotating multi-screw extruder is investigated. The viscosity is assumed to depend on the shear rate and the temperature. The global existence of suitable weak solutions is established. The fictitious domain method which consists in filling the moving rigid screws with the surrounding fluid and taking into account the boundary conditions on these bodies by introducing a well-chosen distribution of boundary forces is used.

MSC:

35Q30 Navier-Stokes equations
35M10 PDEs of mixed type
76U05 General theory of rotating fluids
35D30 Weak solutions to PDEs
76A05 Non-Newtonian fluids
35A01 Existence problems for PDEs: global existence, local existence, non-existence
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