Abstract
This paper characterizes the possible blow-up of solutions for the 3D magneto-hydrodynamics (MHD for short) equations. We first establish some ϵ-regularity criteria in spaces for suitable weak solutions, and then together with an embedding theorem from space into a Morrey type space we characterize the local behaviors of solutions near a potential singular point. More precisely, we show that if is a singular point, then for any r>0 it holds that where is a positive constant independent on ν and p.
Acknowledgments
The authors also thank the reviewers for careful reading and constructive comments.
Disclosure statement
The authors declared that they have no conflicts of interest to this work.