Regularity criteria for the solutions to the 3D MHD equations in the multiplier space |
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Authors: | Yong Zhou Sadek Gala |
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Institution: | 1. Department of Mathematics, Zhejiang Normal University, 321004, Jinhua, Zhejiang, People’s Republic of China 2. Department of Mathematics, University of Mostaganem, Box 227, Mostaganem, 27007, Algeria
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Abstract: | In this paper, some improved regularity criteria for the 3D viscous MHD equations are established in multiplier spaces. It is proved that if the velocity field satisfies $$u \in L^{\frac{2}{1-r}}\left( 0,T,\overset{.}{X}_{r}(\mathbb{R}^{3}) \right) \quad {\rm with}\,r\in 0,1,$$ or the gradient field of velocity satisfies $$\nabla u\in L^{\frac{2}{2-\gamma}}\left(0,T,\overset{.}{X}_{\gamma}(\mathbb{R}^{3}) \right) \quad {\rm with}\,\gamma \in \left 0,1\right],$$ then the solution remains smooth on 0, T]. |
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