Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 13, Issue 1, Pages 410-418Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2011.07.055
Keywords
MHD equations; Regularity criterion
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Funding
- Zhejiang Innovation Project [T200905]
- ZJNSF [R6090109]
- NSFC [10971197]
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In this paper, we establish two new regularity criteria for the 3D incompressible MHD equations involving partial components of the velocity and magnetic fields. It is proved that if u(3), b is an element of L(alpha)(0, T ; L(gamma)(R(3))), 2/alpha + 3/gamma <= 3/4 + 1/2 gamma, gamma > 10/3 or u(3), b is an element of L(alpha 1) (0, T ; L(gamma 1) (R(3))), with 2/alpha(1) + 3/gamma(1) <= 1, 3 < gamma(1) <= infinity, partial derivative(3)u(1), partial derivative(3)u(2) is an element of L(alpha 2) (0, T ; L(gamma 2)(R(3))), with 2/alpha(2) + 3/gamma(2) <= 2, 3/2 < gamma(2) <= infinity, then the local strong solution (u, b) remains smooth on [0, T]. (C) 2011 Elsevier Ltd. All rights reserved.
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