Quasi-neutral limit of Euler–Poisson system of compressible fluids coupled to a magnetic field

In this paper, we consider the quasi-neutral limit of a three-dimensional Euler–Poisson system of compressible fluids coupled to a magnetic field. We prove that, as Debye length tends to zero, periodic initial-value problems of the model have unique smooth solutions existing in the time interval where the ideal incompressible magnetohydrodynamic equations has smooth solution. Meanwhile, it is proved that smooth solutions converge to solutions of incompressible magnetohydrodynamic equations with a sharp convergence rate in the process of quasi-neutral limit.