On Parker instability under L2-norm. (March 2020)

• Record Type: Journal Article
• Authors: Liu, Mengmeng; Song, Fangying; Wang, Weiwei
• Is Part Of: Nonlinear analysis. Volume 192(2020)
• Publication Date: 2020-03
• Subjects: Magnetohydrodynamic fluid -- Parker instability -- Bootstrap instability method; 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.2019.111697
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We mathematically investigate the Parker instability in the three-dimensional compressible isentropic viscous magnetohydrodynamic (MHD) fluid with zero resistivity in the presence of a modified gravitational force in a vertical strip domain in which the velocity of the fluid is non-slip on the boundary. We prove the existence of Parker instability solutions in the sense of L 2 -norm in Lagrangian coordinates based on a classical bootstrap instability method with finer skills of energy estimates. By an inverse transformation of Lagrangian coordinates, we also get Parker instability solutions in L 2 -norm in Eulerian coordinates.