Global well-posedness and decay results to 3D generalized viscous magnetohydrodynamic equations

Abstract

This paper concerns the three-dimensional incompressible generalized magnetohydrodynamic equations. By using the Lei and Lin (Commun Pure Appl Math 64:1297-1304 2011) argument, we get the global well-posedness of the generalized magnetohydrodynamic equations with small initial data. Moreover, we prove that the corresponding global solution decays to zero as time goes to infinity.

Decay rate of global solutions to three dimensional generalized MHD system

“…For the GMHD system (1) with α = β, Ye [21] proved the global well-posedness and decay results with small initial value. Global well-posedness and analyticity results of mild solutions with small initial data are established in [16].…”

Global existence and analyticity of solution for the generalized Hall‐magnetohydrodynamics system

“…∇×((∇× b )× b ) disappears, is reduced to the classical and the generalized MHD system. We emphasize on the global well‐posedness and analytic of solution in the critical space for our purpose, see other studies . We also refer to Lin et al and Liu and Wang for global large solution under a class of large initial data.…”

“…Motivated by the results of previous studies and the above difficulty, the main purpose of this paper is to prove the global existence and analyticity of solutions to with 1/2 ≤ α , β ≤ 1 in the function space . Here, the function space χ s is defined by and the association norm is given by For the details, we may refer to Lei and Lin …”

Well-posedness and decay of solutions to 3D generalized Navier-Stokes equations

“…Accordingly, there are many literatures devoted to find regularity criteria or prove partial regularity for 3D generalized Navier-Stokes system, such as [2,5,32] and [34]. Another direction is to obtain its global existence of strong or smooth solutions for the generalized Navier-Stokes equations or generalized MHD equations with small initial data belonging to a variety of spaces, for example, the pseudomeasure space [22], and the space χ 1−2α [33].…”