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A scaling invariant regularity criterion for the 3D incompressible magneto-hydrodynamics equations

被引：16
|
作者：
Xu, Fuyi [1 ]
Li, Xinliang [1 ]
Cui, Yujun [2 ]
Wu, Yonghong [3 ]
机构：
[1] Shandong Univ Technol, Sch Sci, Zibo 255049, Shandong, Peoples R China
[2] Shandong Univ Sci & Technol, Dept Appl Math, Qingdao 266590, Shandong, Peoples R China
[3] Curtin Univ, Dept Math & Stat, Perth, WA 6845, Australia
来源：
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2017年 / 68卷 / 06期
基金：
中国国家自然科学基金; 中国博士后科学基金;
关键词：
MHD equations; Scaling invariant; Regularity criterion; NAVIER-STOKES EQUATIONS; MHD EQUATIONS; WEAK SOLUTIONS; VORTICITY;
D O I：
10.1007/s00033-017-0874-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we are concerned with the regularity criterion for weak solutions to the 3D incompressible MHD equations. We show that if any two groups functions of (partial derivative(1)u(1), partial derivative(1)b(1)), (partial derivative(2)u(2), partial derivative(2)b(2)) and (partial derivative(3)u(3), partial derivative(3)b(3)) belong to the space L-theta([0, T); L-r(R-3)), 2/theta + 3/r = 2, 3/2 < r <= infinity, then the solution (u, b) to the MHD equations actually is smooth on (0, T).
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页数：8
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