Analyticity and time-decay rate of global solutions for the generalized MHD system near an equilibrium

Existence and analyticity of global mild solutions to GMHD equations with the Coriolis force near an equilibrium

“…In addition to those results mentioned above, when 1 2 ≤ α ≤ β ≤ 1, Ye and Zhao [23] obtained global stability and asymptotic decay of zero solutions. Lu, Li and Wang [13] proved analyticity and time-decay rate of global mild solutions near an equilibrium in the critical space χ 1−2α ∩ χ 1−2β . When Ω = 0 and α = β = 1, (1.1) becomes the classical MHD equations, which has a lot of achievements.…”

“…On the one hand, owing to the existence of linear terms e 3 × u, ∂ l u, and ∂ l b, it is very difficult to deduce the solutions operator and decay property of the solutions operator to the problem (1.3)-(1.4). Based on the solutions operator and decay property of the solutions operator, the existence and analyticity of global solutions to three-dimensional GMHD equations have been proved in [13] and [21]. Fortunately, this difficulty can be overcome by the energy methods and frequency division technology in the Fourier space.…”