两同心旋转球间流动的弱解的存在唯一性

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基金项目: 自然科学基金(19671067);攀登计划资助

The Existence and Uniqueness of Weak Solution of the Flow Between Two Concentric Rotating Spheres

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

摘要: 研究了两个同心旋转球间的轴对称不可压缩的粘性流动.该流动广泛应用于大气物理和地球物理等学科中,为了得到该流动的流函数-速度形式的Navier-Stokes方程的弱解的存在性和唯一性,首先发现了该方程中非线性项之间的关系,并引入一个有限维的辅助问题,通过紧性而得到了结论.
- Navier-Stokes方程 /
- 流函数 /
- Gelerkin方法
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.
- Navier-Stokes equations /
- stream function /
- Galerkin method

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