Applied Mathematics and Mechanics (English Edition) ›› 2000, Vol. 21 ›› Issue (1): 67-72.

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THE EXISTENCE AND UNIQUENESS OF WEAK SOLUTION OF THE FLOW BETWEEN TWO CONCENTRIC ROTATING SPHERES

Feng Weibing1, Li Kaitai2   

  1. 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P R China;
    2. Science School of Xi’an Jiaotong University, Xi’an 710049, P R China
  • Received:1997-08-11 Revised:1999-07-13 Online:2000-01-18 Published:2000-01-18
  • Supported by:

    the National Natural Science Foundation of China(19671067);State Key Basic Research Project

Abstract: 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.

Key words: Navier_Stokes equations, stream function, Galerkin method

2010 MSC Number: 

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