On Conditional Regularity for the MHD Equations via Partial Components

In this paper, we establish new regularity criteria for the three-dimensional (3D) viscous incompressible magnetohydrodynamic (MHD) equations. It is proved that if the solution of the MHD equations satisfies u3∈Lp(0,T;Lq(R3)),j3∈Lr(0,T;Ls(R3)),2p+3q=1324,7213≤q≤∞;2r+3s=2,32<s≤∞ or u3∈Lp(0,T;Lq(R3)),w3∈Lr(0,T;Ls(R3)),2p+3q=1324,7213≤q≤∞;2r+3s=2,32<s≤∞, then the regularity of the solution on (0, T), where u3, j3 and ω3 are the third component of velocity u, current density ∇ × b and vorticity ∇ × u, respectively. These results give new improvements of regularity theory of weak solutions.

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On Conditional Regularity for the MHD Equations via Partial Components

Cited by 4 publications

References 49 publications

Global weighted regularity for the 3D axisymmetric MHD equations

Global weighted regularity for the 3D axisymmetric MHD equations

Regularity criteria of axisymmetric weak solutions to the 3D MHD equations

Improved regularity criteria for the MHD equations

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