Electronic Journal of Differential Equations,
Vol. 2014 (2014), No. 98, pp. 1-18.

Title: Component reduction for regularity criteria of the three-dimensional
       magnetohydrodynamics systems

Author: Kazuo Yamazaki (Oklahoma State Univ., Stillwater, OK, USA)

Abstract:
 We study the regularity of the three-dimensional magnetohydrodynamics
 system, and obtain criteria in terms of one velocity
 field component and two magnetic field components.
 In contrast to the   previous results such as [22], we have eliminated
 the condition on  the third component of the magnetic field completely
 while preserving  the same upper bound on the integrability condition.

Submitted  December 9, 2013. Published April 11, 2014.
Math Subject Classifications: 35B65, 35Q35, 35Q86.
Key Words: Magnetohydrodynamics system; Navier-Stokes equations;
           regularity criteria.