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

作　　者：Xiao Li GUO Yue Yang MEN 

机构地区：[1]Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002, P. R. China [2]Institute of Applied Physics and Computational Mathematics, Beijing 100088, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2017年第12期1632-1646,共15页数学学报（英文版）

摘　　要：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].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].

关 键 词：Stationary Navier-Stokes equations suitable weak solutions partial regularity 

分 类 号：O175[理学—数学]