The analysis of stationary viscous incompressible flow through a rotating radial blade machine, existence of a weak solution

摘要

The paper deals with the analysis of the mathematical model of the two dimensional stationary viscous incompressible flow through a rotating radial blade machine. The flow is described and studied in the rotating frame. The paper provides the classical and weak formulation of the corresponding boundary value problem. The boundary condition on the outflow is the so called “natural” boundary condition, with the nonlinear term proposed by Bruneau and Fabrie (1996) [1], and also modified by a term arising from the rotation of the machine. The existence of a weak solution is proved.