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Title: Remarks on the regularity criteria of three-dimensional magnetohydrodynamics system in terms of two velocity field components

We study the three-dimensional magnetohydrodynamics system and obtain its regularity criteria in terms of only two velocity vector field components eliminating the condition on the third component completely. The proof consists of a new decomposition of the four nonlinear terms of the system and estimating a component of the magnetic vector field in terms of the same component of the velocity vector field. This result may be seen as a component reduction result of many previous works [C. He and Z. Xin, “On the regularity of weak solutions to the magnetohydrodynamic equations,” J. Differ. Equ. 213(2), 234–254 (2005); Y. Zhou, “Remarks on regularities for the 3D MHD equations,” Discrete Contin. Dyn. Syst. 12(5), 881–886 (2005)].
Authors:
 [1]
  1. Department of Mathematics, Oklahoma State University, 401 Mathematical Sciences, Stillwater, Oklahoma 74078 (United States)
Publication Date:
OSTI Identifier:
22251044
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EQUATIONS; MAGNETOHYDRODYNAMICS; NONLINEAR PROBLEMS; THREE-DIMENSIONAL CALCULATIONS; VECTOR FIELDS; VELOCITY