On classical solutions to the Cauchy problem of the 2D compressible non-resistive MHD equations with vacuum states. (17th August 2017)

• Record Type: Journal Article
• Authors: Chen, Mingtao; Zang, Aibin
• Is Part Of: Nonlinearity. Volume 30:Number 9(2017:Sep.)
• Page Start: 3637
• Page End: 3675
• Publication Date: 2017-08-17
• Subjects: 2D compressible non-resistive MHD equations -- vacuum -- classical solutions -- blowup criterion; 35Q35 (35B44 76W05); Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aa7e97
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: In this paper, we investigate the Cauchy problem of the compressible non-resistive MHD on R 2 with a vacuum as the far field density. We prove that the two-dimensional (2D) Cauchy problem has a unique local strong solution provided that the initial density and magnetic field decay are not too slow at infinity. Furthermore, if the initial data satisfies some additional regularity and compatibility conditions, the strong solution becomes a classical one. Additionally, we establish a blowup criterion for the 2D compressible non-resistive MHD depending solely on the density and magnetic fields.