On the blow-up criterion of strong solutions for the MHD equations with the Hall and ion-slip effects in $${\mathbb{R}^{3}}$$ R 3

Abstract

Abstract. In this paper, we establish a blow-up criterion of strong solutions to the 3D incompressible magnetohydrodynamics equations including two nonlinear extra terms: the Hall term (quadratic with respect to the magnetic field) and the ion-slip term (cubic with respect to the magnetic field). This is an improvement of the recent results given by Fan et al. (Z Angew Math Phys, 2015).

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

“…It is quite rare to prove the existence of large, smooth, global solutions for quasilnear system. Under a class of large initial data, we found some results for incompressible Navier-Stokes equations, the incompressible MHD equations, and the incompressible Hall-MHD equations; see previous studies 8,9,11,13,18,[24][25][26][27][28][29][30][31][32][33][34][35][36] for details. Those motivate us to study the global well-posedness of the Cauchy problem of Equation (1.1) with large initial data.…”