Abstract
In this article, we consider the existence of discretely self-similar solutions and self-similar solutions to the 3D generalized magnetohydrodynamics (MHD) system with fractional dissipative terms (−Δ)αv and (−Δ)αH, 78<α<54. Using the Brouwer fixed-point theorem and Littlewood analysis method, we prove the global existence of discretely self-similar solutions and self-similar solutions to the 3D generalized MHD system when the initial data are in the critical space Lw32α−1 or the critical Besov space Ḃp,∞1−2α+3p, where 32α−1<p<65−4α, p<3α−1 when 76≤α<54.
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