The existence and uniqueness of weak solution of the flow between two concentric rotating spheres

The unsteady axisymmetric incompressible flow between two concentric spheres was discussed in this paper. It is useful to most astrophysical, geophysical and engineering applications. In order to get the existence and uniqueness of weak solution of this flow with the stream_velocity form, firstly, the relations among the nonlinear terms in this equation is found; then, the existence is proved by an auxiliary semi_discrete scheme and a compactness argument.