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$(N-1)$ velocity components condition for the generalized MHD system in $N-$dimension

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  • We study the magnetohydrodynamics system, generalized via a fractional Laplacian. When the domain is in $N-$dimension, $N$ being three, four or five, we show that the regularity criteria of its solution pair may be reduced to $(N-1)$ many velocity field components with the improved integrability condition in comparison to the result in [29]. Furthermore, we extend this result to the three-dimensional magneto-micropolar fluid system.
    Mathematics Subject Classification: Primary: 35B65, 35Q35; Secondary: 35Q86.

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