On a mathematical model of journal bearing lubrication

We consider the 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 nonhomogeneous Dirichlet, Navier’s slip and inflow/outflow parts. We prove the existence of weak solutions and show that the resulting level of the pressure is fixed by the boundary conditions. The problem is motivated by particular applications from tribology.