On partial regularity of suitable weak solutions to the stationary fractional Navier–Stokes equations in dimension four and five
On partial regularity of suitable weak solutions to the stationary fractional Navier–Stokes equations in dimension four and five
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DOI：
10.1007/s10114-017-7125-z
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发表时间：
2017-11
期刊：
影响因子：
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通讯作者：
Xiaohai Guo;Yueyang Men
中科院分区：
文献类型：
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作者：
Xiaohai Guo;Yueyang Men
本文研究了具有Laplacian（−Δ）α（n/6 ≤α< 1，α <$1/2）分数幂的多维定常Navier-Stokes方程适当弱解的部分正则性.证明了该系统的适当弱解的可能奇点集的+2 − 6α（3 ≤n≤ 5）维Hausdorff测度为零，推广了Tang和Yu [19]的结果到四维和五维.此外，ε-正则性准则中的压力是文[1，13，18，20]中相应结果的改进.
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 (−Δ)α(n/6 ≤α< 1 andα≠ 1/2). It is shown that then+ 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 inε-regularity criteria is an improvement of corresponding results in [1, 13, 18, 20].