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Global well-posedness of the generalized magnetohydrodynamic equations. (English) Zbl 1404.35374
Summary: In this paper, we establish the global existence of mild solutions to the \(n\)-dimensional generalized MHD system provided that the norms of the initial data are bounded exactly by the minimal value of the viscosity coefficients and the fractional powers. In addition, we also establish the existence of the global small solution in the Fourier-Herz spaces. Finally, we prove the long time decay of the global solutions in the corresponding spaces.

MSC:
35Q35 PDEs in connection with fluid mechanics
35B65 Smoothness and regularity of solutions to PDEs
76W05 Magnetohydrodynamics and electrohydrodynamics
35R11 Fractional partial differential equations
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