A double-logarithmically improved regularity criterion of weak solutions for the 3D MHD equations

This paper devotes to establish an improved regularity criterion for weak solution of 3D incompressible MHD equations. We show that the weak solution is regular, provided that ∫0T‖π(·,t)‖B˙∞,∞-12(e+ln(e+‖π(·,t)‖B˙∞,∞-1))ln(e+ln(e+‖π(·,t)‖B˙∞,∞-1))dt<∞.As a consequence, this improves some previous works. © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.