Global existence and exponential stability of solutions for planar compressible Hall-magnetohydrodynamic equations

An initial-boundary value problem for Hall-magnetohydrodynamics in one space dimension with general large initial data is investigated. We establish uniform pointwise positive lower and upper bounds of the density, which are independent of any length of time. Based on the bounds of the density and the skew-symmetric structure of the Hall term, we derive the global existence, uniqueness and exponential stability of strong solutions.