In this article, we consider the tridimensional generalized Hall magneto-hydrodynamics (Hall-MHD) system, with and . For , , we obtain the global regularity of classical solutions. For and , with small data, the system also possesses global classical solutions. In addition, for the standard Hall-MHD system, , by adding a suitable condition, we give a positive answer to the open question in . At last, we study the regularity criterions of generalized Hall-MHD system. In particular, we prove the regularity criterion in terms of horizontal gradient for , .
Submitted November 11, 2014. Published June 29, 2015.
Math Subject Classifications: 35Q35, 35B65, 76W05.
Key Words: Generalized Hall-mhd system; global regularity; classical solutions.
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| Renhui Wan |
Department of mahtematics
Hangzhou, Zhejiang 310027, China
email: email@example.com, firstname.lastname@example.org
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