On Parker instability under L2-norm. (March 2020) - Liu, Mengmeng; Song, Fangying; Wang, Weiwei
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.