Navier’s slip and evolutionary Navier-Stokes-like systems with pressure and shear-rate dependent viscosity. (English) Zbl 1129.35055

One investigates the mathematical properties of internal unsteady three-dimensional flows of fluids with viscosity depending on the shear rate as well as the pressure. The fluids are subject to Navier’s slip at the boundary. One establishes the long-time existence of a weak solution for large data provided that the viscosity depends on the shear rate and the pressure in a suitably specified manner. This specific relationship however includes the classical Navier-Stokes fluids and power law fluids (with power law index \(r-2\), \(r\leq 2\)) as special cases. For these special cases, the presented existence results are new in the literature.


35Q30 Navier-Stokes equations
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76A05 Non-Newtonian fluids
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