Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2018; 55(3): 735-747

Online first article April 3, 2018      Printed May 31, 2018

https://doi.org/10.4134/BKMS.b170088

Copyright © The Korean Mathematical Society.

Asymptotic behavior of solutions for the generalized MHD and Hall-MHD systems in $\mathbb{R}^n$

Mingxuan Zhu

Jiaxing University

Abstract

This paper deals with the asymptotic behavior of solutions to the generalized MHD and Hall-MHD systems. Firstly, the upper bound for the generalized MHD and Hall-MHD systems is investigated in $L^2$ space. Then, the effect of the Hall term is analyzed. Finally, we optimize the upper bound of decay and obtain their algebraic lower bound for the generalized MHD system by using Fourier splitting method.

Keywords: generalized MHD system, generalized Hall-MHD system, asymptotic behavior, upper bound, lower bound

MSC numbers: 35Q35, 35B65, 76D05