On the non-resistive limit and the magnetic boundary-layer for one-dimensional compressible magnetohydrodynamics. (17th August 2017)

• Record Type: Journal Article
• Authors: Jiang, Song; Zhang, Jianwen
• Is Part Of: Nonlinearity. Volume 30:Number 9(2017:Sep.)
• Page Start: 3587
• Page End: 3612
• Publication Date: 2017-08-17
• Subjects: compressible MHD equations -- non-resistive limit -- magnetic boundary-layer -- global well-posedness -- initial-boundary value problem; 35M10 -- 35Q60 -- 76N10 -- 76N17 -- 76N20; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aa82f2
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We consider an initial-boundary value problem for the one-dimensional equations of compressible isentropic magnetohydrodynamic (MHD) flows. The non-resistive limit of the global solutions with large data is justified. As a by-product, the global well-posedness of the compressible non-resistive MHD equations is established. Moreover, the thickness of the magnetic boundary-layer of the value O ( ν α ) with 0 < α < 1 / 2 is proved, where ν > 0 is the resistivity coefficient. The proofs of these results are based on a full use of the so-called 'effective viscous flux', the material derivative and the structure of the equations.