Affiliation:
1. School of Mathematics and Statistics, Central South University, Changsha, 410083 Hunan, P.R. China. E-mails: math120701012cz@163.com, fengwx0118@163.com, qindd132@163.com
Abstract
In this paper we consider the following 2D MHD system with horizontal dissipation in a strip domain T × R. ∂ t u + u · ∇ u + ∂ 11 u + ∇ p = b · ∇ b , ∂ t b + u · ∇ b + ∂ 11 b = b · ∇ u , ∇ · u = ∇ · b = 0 , u ( 0 ) = u 0 ( x ) , b ( 0 ) = b 0 ( x ) . A bootstrapping argument together with a more accurate energy functional is employed in order to get the stability for the above system. Moreover, using a suitable transform, we also investigate the 2D MHD system with vertical dissipation in a strip domain R × T.