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

作者：Xu, Fuyi^*

来源：Journal of Mathematical Analysis and Applications, 2018, 460(2): 634-644.

DOI：10.1016/j.jmaa.2017.12.017

• MHD equations
• Regularity criterion
• Littlewood-Paley decomposition

The paper is dedicated to study of the regularity criterion for weak solutions to the 3D incompressible MHD equations. Employing the Littlewood Paley decomposition, we show that if (del) over bar(u) over bar = (partial derivative(1)(u) over bar, partial derivative(2)(u) over bar) is an element of L-partial derivative 1 ([0, T); B-r1,2r/3(0) (R-3)), 2/r(1) + 3/r(1) = 2,3/2 <r(1) <= infinity and <(del)over bar>(b) over bar = (partial derivative(1)(b) over bar, partial derivative(2)(b) over bar) is an element of L-partial derivative 1 ([0, T); B-r1,2r/3(0) (R-3)), 2/r(1) + 3/r(1) = 2,3/2 <r(1) <= infinity, then the solutions to the MHD actually is smooth on (0,T).

• 出版日期2018-4-15
• 单位山东理工大学