Global well-posedness of non-resistive quantum MHD system

Abstract

We are concerned with the global well-posedness of viscous non-resistive compressible quantum magnetohydrodynamic (QMHD) system in Lagrangian coordinates. By using a two-tier energy method, we study an initial-boundary value problem of compressible QMHD system in an infinite flat layer. We prove the global existence, uniqueness and decay estimate of smooth solution to the system around a suitably small uniform magnetic field which is non-parallel to the layer.