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A regularity criterion for the density‐dependent magnetohydrodynamic equations
Author(s) -
Zhou Yong,
Fan Jishan
Publication year - 2009
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1255
Subject(s) - magnetohydrodynamic drive , mathematics , smoothness , integrable system , mathematical analysis , vector field , nonlinear system , coupling (piping) , magnetohydrodynamics , mathematical physics , magnetic field , physics , geometry , quantum mechanics , mechanical engineering , engineering
In this paper, regularity criterion for the 3‐D density‐dependent magnetohydrodynamic equation is considered. It is proved that the solution keeps smoothness only under an integrable condition on the velocity field in multiplier spaces. Hence, it turns out that the velocity field plays a dominant role in the regularity criteria of the weak solutions to this nonlinear coupling problem even with density. Copyright © 2009 John Wiley & Sons, Ltd.