Electron. J. Diff. Equ., Vol. 2014 (2014), No. 98, pp. 1-18.

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

Kazuo Yamazaki

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.

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Kazuo Yamazaki
Department of Mathematics, Oklahoma State University
401 Mathematical Sciences, Stillwater, OK 74078, USA
email: kyamazaki@math.okstate.edu

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