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 Asymptotic behavior of solutions for the generalized MHD and Hall-MHD systems in $\mathbb{R}^n$ Bull. Korean Math. Soc. 2018 Vol. 55, No. 3, 735-747 https://doi.org/10.4134/BKMS.b170088Published online May 31, 2018 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 Downloads: Full-text PDF