Lower Bounds of Possible Blow‐Up Solutions of the Electron Magnetohydrodynamics Equations

ABSTRACT In this paper, we investigate the blow‐up rates of strong solutions to the electron magnetohydrodynamics (EMHD) equations. The optimal lower bounds of potential blow‐up solutions of the EMHD equations in homogeneous Sobolev spaces are shown, where for spatial dimensions . Moreover, for , the blow‐up rates of solutions in this system in spaces are also obtained. The proof relies on the cancellation of the Hall term and Kato–Ponce commutator estimate in the homogeneous setting.