PARTIAL REGULARITY OF STATIONARY NAVIER-STOKES SYSTEMS UNDER NATURAL GROWTH CONDITION

doi:10.1007/s10473-019-0110-0

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (1): 94-110.doi: 10.1007/s10473-019-0110-0

PARTIAL REGULARITY OF STATIONARY NAVIER-STOKES SYSTEMS UNDER NATURAL GROWTH CONDITION

何莲花^1,2, 谭忠³

1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;
2. School of Mathematics Science, Guizhou Normal University, Guiyang 550001, China;
3. School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and Scientific Computing, Xiamen University, Xiamen 361005, China

收稿日期:2017-10-23 修回日期:2018-02-05 出版日期:2019-02-25 发布日期:2019-03-13
通讯作者: Zhong TAN E-mail:tan85@xmu.edu.cn
作者简介:Lianhua HE,hlh1981@126.com
基金资助:
The second author was supported by the National Natural Science Foundation of China (11271305, 11531010).

PARTIAL REGULARITY OF STATIONARY NAVIER-STOKES SYSTEMS UNDER NATURAL GROWTH CONDITION

Lianhua HE^1,2, Zhong TAN³

1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;
2. School of Mathematics Science, Guizhou Normal University, Guiyang 550001, China;
3. School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and Scientific Computing, Xiamen University, Xiamen 361005, China

Received:2017-10-23 Revised:2018-02-05 Online:2019-02-25 Published:2019-03-13
Contact: Zhong TAN E-mail:tan85@xmu.edu.cn
Supported by:
The second author was supported by the National Natural Science Foundation of China (11271305, 11531010).

摘要/Abstract

摘要： In this article, we consider the partial regularity of stationary Navier-Stokes system under the natural growth condition. Applying the method of A-harmonic approximation, we obtain some results about the partial regularity and establish the optimal Hölder exponent for the derivative of a weak solution on its regular set.

关键词: partial regularity, Navier-Stoke systems, natural growth condition, A-harmonic approximation

Abstract: In this article, we consider the partial regularity of stationary Navier-Stokes system under the natural growth condition. Applying the method of A-harmonic approximation, we obtain some results about the partial regularity and establish the optimal Hölder exponent for the derivative of a weak solution on its regular set.

Key words: partial regularity, Navier-Stoke systems, natural growth condition, A-harmonic approximation

何莲花, 谭忠. PARTIAL REGULARITY OF STATIONARY NAVIER-STOKES SYSTEMS UNDER NATURAL GROWTH CONDITION[J]. 数学物理学报(英文版), 2019, 39(1): 94-110.

Lianhua HE, Zhong TAN. PARTIAL REGULARITY OF STATIONARY NAVIER-STOKES SYSTEMS UNDER NATURAL GROWTH CONDITION[J]. Acta mathematica scientia,Series B, 2019, 39(1): 94-110.

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PARTIAL REGULARITY OF STATIONARY NAVIER-STOKES SYSTEMS UNDER NATURAL GROWTH CONDITION

PARTIAL REGULARITY OF STATIONARY NAVIER-STOKES SYSTEMS UNDER NATURAL GROWTH CONDITION

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