engleski

Derivation of Non-linear Reynolds-type Problem for Lubrication of a Rotating Shaft

We consider the non-Newtonian flow in a thin domain between a rotating shaft and lubricated support, governed by injection of a fluid. The flow is described by the 3D incompressible Navier-Stokes (Stokes) system with a nonlinear viscosity, being a power of the shear rate (power law). We consider the limit when domain thickness tends to zero and prove that the limit pressure satisfies the non-linear two-dimensional Reynolds lubrication equation. Furthermore, we prove a convergence theorem for the velocity and the pressure in appropriate function spaces.

non-Newtonian flow; non-linear Reynolds problem; power law

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