Blow-up criterion for two-dimensional viscous, compressible, and heat conducting magnetohydrodynamic flows. (July 2016)

• Record Type: Journal Article
• Authors: Lu, Li; Chen, Yajin; Huang, Bin
• Is Part Of: Nonlinear analysis. Volume 139(2016)
• Page Start: 55
• Page End: 74
• Publication Date: 2016-07
• Subjects: 76W05 -- 35B65; Full compressible MHD equations -- Strong solution -- Blow-up criterion; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.02.021
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper establishes a blow-up criterion for the two-dimensional (2D) viscous, compressible, and heat conducting magnetohydrodynamic(MHD) flows. It is essentially shown that for the initial boundary value problem of the 2D full compressible MHD flows with initial density allowed to vanish, the strong solution exists globally if the divergence of velocity satisfies ‖ div u ‖ L 1 ( 0, T ; L ∞ ) < ∞ . In particular, the criterion is independent of both the temperature and the magnetic field and is just the same as that of the full compressible Navier–Stokes equations.