数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (3): 835-854.doi: 10.1007/s10473-020-0317-0

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PARTIAL REGULARITY FOR STATIONARY NAVIER-STOKES SYSTEMS BY THE METHOD OF A-HARMONIC APPROXIMATION

戴祎琛1, 谭忠2   

  1. 1 School of Mathematical Sciences, Xiamen University, Fujian 361005, China;
    2 School of Mathematical Science and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Fujian 361005, China
  • 收稿日期:2019-02-11 出版日期:2020-06-25 发布日期:2020-07-17
  • 作者简介:Yichen DAI,E-mail:yichendai0613@163.com;Zhong TAN,E-mail:tan85@xmu.edu.cn

PARTIAL REGULARITY FOR STATIONARY NAVIER-STOKES SYSTEMS BY THE METHOD OF A-HARMONIC APPROXIMATION

Yichen DAI1, Zhong TAN2   

  1. 1 School of Mathematical Sciences, Xiamen University, Fujian 361005, China;
    2 School of Mathematical Science and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Fujian 361005, China
  • Received:2019-02-11 Online:2020-06-25 Published:2020-07-17

摘要: In this article, we prove a regularity result for weak solutions away from singular set of stationary Navier-Stokes systems with subquadratic growth under controllable growth condition. The proof is based on the A-harmonic approximation technique. In this article, we extend the result of Shuhong Chen and Zhong Tan[7] and Giaquinta and Modica[18] to the stationary Navier-Stokes system with subquadratic growth.

关键词: Stationary Navier-Stokes systems, controllable growth condition, partial regularity, A-harmonic approximation

Abstract: In this article, we prove a regularity result for weak solutions away from singular set of stationary Navier-Stokes systems with subquadratic growth under controllable growth condition. The proof is based on the A-harmonic approximation technique. In this article, we extend the result of Shuhong Chen and Zhong Tan[7] and Giaquinta and Modica[18] to the stationary Navier-Stokes system with subquadratic growth.

Key words: Stationary Navier-Stokes systems, controllable growth condition, partial regularity, A-harmonic approximation

中图分类号: 

  • 35J60