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Note on global regularity of 3D generalized magnetohydrodynamic-$\alpha$ model with zero diffusivity

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  • In this paper we consider the Cauchy problem of a three-dimensional incompressible magnetohydrodynamic-$\alpha$ (MHD-$\alpha$) model with fractional velocity and zero magnetic diffusivity. We prove the global existence results of classical solutions for the model in the endpoint case with arbitrarily large initial data in Sobolev spaces.
    Mathematics Subject Classification: 35Q35, 76D03,.


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