Existence and uniqueness of global strong solutions to the Navier-Stokes-Maxwell system with large initial data and vacuum

Abstract

In this paper, we investigate the initial boundary value problem to the system of the compressible Navier-Stokes equations coupled with the Maxwell equations through the Lorentz force in one space dimension. The global existence and uniqueness of strong solutions with large initial data are established when there is initial vacuum. Our result may be the first result about the global strong solution with large initial data and vacuum.