On global existence, energy decay and blow-up criteria for the Hall-MHD system

Abstract

In this paper, we obtain global existence and energy decay for 3D Hall-magnetohydrodynamics (Hall-MHD) system with − u and − B. Besides the classical energy method and Besov space techniques, the interpolating inequalities are crucial in the proof of decay estimates. Then two Osgood type blow-up criteria are established. Our results improve the corresponding theorems in [3] and [4]. In addition, we establish two Beale-Kato-Majda blow-up criterion for the generalized version of Hall-MHD with − u and (− ) β B, β > 1.

The continuous dependence for the Hall-MHD equations with fractional magnetic diffusion

“…Recently, there are many researches on the standard Hall-MHD equations with −∆u and −∆b , concerning global weak solutions [1], local and global (small) strong solutions [2,3], and the large time behavior of weak and strong solutions [4,5,6,7]. For the system (1.1), Chae, Wan and Wu [8] proved the local existence and uniqueness of the solution to the Hall-MHD equations with only a fractional Laplacian magnetic diffusion…”

Global existence and temporal decay for the 3D compressible Hall-magnetohydrodynamic system

“…When ρ = const, system (1.1) becomes the incompressible Hall-MHD system, which has received many studies, see [1,4,5,6,13,14,17,36,37,38]. When divu = 0, system (1.1) becomes the density-dependent Hall-MHD system, which has been investigated by many authors, and for more details, see [12,18].…”

Global existence and zero α limit of the 3D incompressible two‐fluid MHD equations

“…In [14], Chae and Lee established two improved blow-up criteria and two global existence results of the classical solutions for small initial data. Some relevant results about Hall-MHD equations can be found in [15][16][17][18][19][20][21][22][23].…”