On Partial Regularity of Suitable Weak Solutions to the Stationary Fractional Navier-Stokes Equations in Dimension Four and Five

In this paper, we investigate the partial regularity of suitable weak solutions to the multi- dimensional stationary Navier-Stokes equations with fractional power of the Laplacian （-△）^α （n/6 ≤α〈1 and a ≠ 1/2）. It is shown that the n ＋ 2 - 6α （3 ≤ n ≤5） dimensional Hausdorff measure of the set of th...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2017-12, Vol.33 (12), p.1632-1646
Main Authors: Guo, Xiao Li, Men, Yue Yang
Format: Article
Language:English
Subjects:
Fluid dynamics
Fluid flow
Hausdorff测度
Laplace transforms
Mathematical analysis
Mathematics
Mathematics and Statistics
Navier-Stokes equations
Regularity
Stokes方程
分数
局部正则性
弱解
斯托克斯方程
正则性准则
部分正则性
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Summary:In this paper, we investigate the partial regularity of suitable weak solutions to the multi- dimensional stationary Navier-Stokes equations with fractional power of the Laplacian （-△）^α （n/6 ≤α〈1 and a ≠ 1/2）. It is shown that the n ＋ 2 - 6α （3 ≤ n ≤5） dimensional Hausdorff measure of the set of the possible singular points of suitable weak solutions to the system is zero, which extends a recent result of Tang and Yu [19] to four and five dimension. Moreover, the pressure in ε-regularity criteria is an improvement of corresponding results in [1, 13, 18, 20].
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-017-7125-z