Singular limits of the equations of compressible ideal magneto-hydrodynamics in a domain with boundaries

Article type: Research Article

Authors: Ju, Qiangchang^a | Schochet, Steve^b | Xu, Xin^{b; *}

Affiliations: [a] Institute of Applied Physics and Computational Mathematics, Beijing 100088, P.R. China. E-mail: ju_qiangchang@iapcm.ac.cn | [b] School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel. E-mails: schochet@tauex.tau.ac.il, xuxinaboy@126.com

Correspondence: [*] Corresponding author. E-mail: xuxinaboy@126.com.

Abstract: Singular limits of the equations of compressible ideal magneto-hydrodynamics with physical boundary conditions are considered. The uniform existence of classical solutions with respect to the Mach number and Alfvén number is established by energy methods. Under appropriate conditions on the initial data, convergence of the solutions of the original system is proved as the two small parameters tend to zero with the limiting solutions satisfying the two-dimensional incompressible flow.

Keywords: Compressible ideal magneto-hydrodynamics, Mach number, Alfvén number, singular limits

DOI: 10.3233/ASY-181509

Journal: Asymptotic Analysis, vol. 113, no. 3, pp. 137-165, 2019