Asymptotic behavior of global smooth solutions for bipolar compressible Navier-Stokes-Maxwell system from plasmas

This paper is concerned with the bipolar compressible Navier-Stokes-Maxwell system for plasmas. We investigated, by means of the techniques of symmetrizer and elaborate energy method, the Cauchy problem in ℝ3. Under the assumption that the initial values are close to a equilibrium solutions, we prove that the smooth solutions of this problem converge to a steady state as the time goes to the infinity. It is shown that the difference of densities of two carriers converge to the equilibrium states with the norm ‖.‖Hs-1, while the velocities and the electromagnetic fields converge to the equilibrium states with weaker norms than ‖.‖Hs-1. This phenomenon on the charge transport shows the essential difference between the unipolar Navier-Stokes-Maxwell and the bipolar Navier-Stokes-Maxwell system.