Global well-posedness of the 2-D magnetic Prandtl model in the Prandtl–Hartmann regime

Article type: Research Article

Authors: Chen, Dongxiang^a | Ren, Siqi^b | Wang, Yuxi^b | Zhang, Zhifei^{b; *}

Affiliations: [a] College of Mathematics and Information Science, Jiangxi Normal University, 330022, Nanchang, P.R. China. E-mail: chendx020@aliyun.com | [b] School of Mathematical Sciences, Peking University, 100871, Beijing, P.R. China. E-mails: 415333144@qq.com, wangyuxi0422@pku.edu.cn, zfzhang@math.pku.edu.cn

Correspondence: [*] Corresponding author. E-mail: zfzhang@math.pku.edu.cn.

Abstract: In this paper, we prove the global well-posedness of the 2-D magnetic Prandtl model in the mixed Prandtl/Hartmann regime when the initial data is a small perturbation of the Hartmann layer in Sobolev space.

Keywords: Magnetic Prandtl equation, Hartmann layer, MHD equations, global stability

DOI: 10.3233/ASY-191593

Journal: Asymptotic Analysis, vol. 120, no. 3-4, pp. 373-393, 2020