Abstract
In this paper, we establish some improved regularity conditions for the three-dimensional (3D) magnetohydrodynamics equations. We proved the logarithmically improved Caflisch–Klapper–Steele’s criteria [“Remarks on sigularities, dimension and energy dissipation for ideal hydrodynamics and MHD,” Commun. Math. Phys. 184, 443 (1997)] as well as the logarithmically improved He–Xin’s [“On the regularity of weak solutions to the magnetohydrodynamic equations,” J. Differ. Equ. 23, 235 (2005)] and Wu’s [“Bounds and new approach for the 3D MHD equations,” J. Nonlinear Sci. 12, 395 (2002)] results for 3D ideal MHD equations.
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