Global Regularity of 2D Generalized MHD Equations with Magnetic Diffusion

This paper is concerned with the global regularity of the 2D (two-dimensional) generalized magnetohydrodynamic equations with only magnetic diffusion $Λ^{2β} b$. It is proved that when $β>1$ there exists a unique global regular solution for this equations. The obtained result improves the previous known one which requires that $β>\frac32$.

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