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To study the regularity criteria of solutions, the three-dimensional axially symmetric incompressible magnetohydrodynamics (MHD) equations with swirl are presented. Two types of particular weak solutions to the three-dimensional axially symmetric incompressible MHD equations uθ=0, Br=Bz=0, and Br=Bz=0 are considered. By using the energy method and the embedding method, the regularity criteria for the two types of weak solutions to the three-dimensional axially symmetric incompressible MHD equations are obtained if the radial direction component ur satisfies some conditions. ©, 2015, Beijing University of Technology. All right reserved.
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