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 L2-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 L2-norm in Eulerian coordinates.
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