Global well-posedness and asymptotic behavior of solutions for the three-dimensional MHD equations with Hall and ion-slip effects

A class of global large, smooth solutions for the magnetohydrodynamics with the Hall and ion-slip effects

“…Comparing with [14,34], our result can be seen as an non-trival improvement of Fan et al's and Zhao et al's work, for we completely drops the smallness condition on the initial data.…”

“…Recently, Fan et.al in [14] established global existence and time decay for small solutions. Very recently, Zhao and Zhu in [34] gave a proof of global existence for small solutions under weaker smallness conditions. However, none of results are known for MHD system with the Hall and ion-slip effects for general initial data without smallness conditions.…”

Asymptotic behavior of solutions to incompressible electron inertial Hall-MHD system in $ \mathbb{R}^3 $

“…There are some other papers studied the decay characterization of dissipative equations (cf. [23,9,5,32,34] and the reference therein). For more details on P r and r * , we refer to Section 2.…”

A class of global large, smooth solutions for the magnetohydrodynamics with Hall and ion‐slip effects

“…[19][20][21] For global solutions, Fan et al 22 established global existence and time decay for small solutions. Very recently, Zhao and Zhu 23 gave a proof of global existence for small solutions under weaker smallness conditions. However, none of results are known for MHD system with the Hall and ion-slip effects for general initial data without smallness conditions.…”