Stability for the 2D MHD equations with horizontal dissipation

Article type: Research Article

Authors: Chen, Zhi | Feng, Weixun | Qin, Dongdong^{; *}

Affiliations: School of Mathematics and Statistics, Central South University, Changsha, 410083 Hunan, P.R. China

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: In this paper we consider the following 2D MHD system with horizontal dissipation in a strip domain T×R. ∂tu+u·∇u+∂11u+∇p=b·∇b,∂tb+u·∇b+∂11b=b·∇u,∇·u=∇·b=0,u(0)=u0(x),b(0)=b0(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.

Keywords: 2D MHD system, horizontal dissipation, vertical dissipation, strip domain

DOI: 10.3233/ASY-211733

Journal: Asymptotic Analysis, vol. 129, no. 3-4, pp. 361-377, 2022