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Note on global regularity of 3D generalized magnetohydrodynamic-\(\alpha\) model with zero diffusivity. (English) Zbl 1314.35114
Summary: 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.

MSC:
35Q35 PDEs in connection with fluid mechanics
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76W05 Magnetohydrodynamics and electrohydrodynamics
35R11 Fractional partial differential equations
35B65 Smoothness and regularity of solutions to PDEs
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