A refined regularity criterion for the strong solution to the Leray-alpha-MHD equation

作者：Chen, Xiaoli^*; Chen, Dongxiang

来源：Mathematical Methods in the Applied Sciences, 2018, 41(17): 7958-7970.

DOI：10.1002/mma.5258

• Leray-alpha-MHD equation
• Morrey-Campanato space
• regularity criterion
• strong solution

This paper establishes a regularity criterion for the strong solution to the Leray-alpha-MHD in Campanato-Morrey space. We show that if the magnetic field b satisfies the following condition: integral(T)(0) parallel to del b(tau,.)parallel to(2p/2p-3)(Mqp) + parallel to D(2)b(tau,.)parallel to(2p/2p-3)(Mqp) d tau < infinity, the strong solution (v, b) to the 3-D Leray-alpha MHD equation can be extended beyond T > 0. We also prove that if the magnetic field b satisfies integral(T)(0) parallel to del b(tau,.)parallel to(p/p-1)(Mqp) d tau < infinity, the strong solution (v, b) to the 2-D Leray-alpha MHD equation can be extended beyond T > 0, which extends the results in previous studies.

• 出版日期2018-11-30
• 单位江西师范大学