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Regularity criteria for a magnetohydrodynamic-$\alpha$ model

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  • We study the $n$-dimensional magnetohydrodynamic-$\alpha$ (MHD-$\alpha$) model in the whole space. Various regularity criteria are established. When $n=4$, uniqueness of weak solutions is also proved. As a corollary, the strong solution to this model exists globally, as $n \leq 4$.
    Mathematics Subject Classification: Primary: 35B40, 76D03.

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