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On a mathematical model of journal bearing lubrication. (English) Zbl 1237.76038

The authors consider the isothermal steady motion of an incompressible fluid whose viscosity depends on the pressure and the shear rate. The system is completed by suitable boundary conditions involving non-homogeneous Dirichlet, Navier’s slip and inflow/outflow parts. The authors prove the existence of weak solutions and show that the resulting level of the pressure is fixed by the boundary conditions. The paper is motivated by the journal bearing lubrication problem and extends the earlier results for homogeneous boundary conditions.

MSC:

76D08 Lubrication theory
76A05 Non-Newtonian fluids
35Q35 PDEs in connection with fluid mechanics
35J65 Nonlinear boundary value problems for linear elliptic equations
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
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