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Global Existence and Large Time Behavior of Solutions to 3D MHD System Near Equilibrium.

Authors :
Xiao, Yamin
Yuan, Baoquan
Source :
Results in Mathematics / Resultate der Mathematik; May2021, Vol. 76 Issue 2, p1-20, 20p
Publication Year :
2021

Abstract

In this paper, we consider the stability problem on perturbation near a physically steady state solution of the 3D generalized incompressible magnetohydrodynamic system in Lei-Lin space. The global stability and analytic estimates for small perturbation are established by the semigroup method in the critical space χ 1 - 2 α (R 3) with 1 2 ≤ α ≤ 1 , where linear terms from perturbation incur much difficulty. By introducing a diagonalization process we successfully eliminate the linear terms. Then, by virtue of the analytic estimates for a solution, the temporal decay rate (1 + t) - (5 4 α - 1) of the global solution is obtained. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
14226383
Volume :
76
Issue :
2
Database :
Complementary Index
Journal :
Results in Mathematics / Resultate der Mathematik
Publication Type :
Academic Journal
Accession number :
150326558
Full Text :
https://doi.org/10.1007/s00025-021-01382-w