Asymptotic behavior of global smooth solutions for bipolar compressible Navier-Stokes-Maxwell system from plasmas. Issue 5 (September 2015) - FENG, Yuehong; WANG, Shu; LI, Xin
Abstract 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 <alternatives><inline-graphic xlink:href="ark:/27927/pgj28jbmfw6" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />ℝ3</alternatives>. 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 <alternatives><inline-graphic xlink:href="ark:/27927/pgj28jbmg31" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />‖.‖Hs-1</alternatives>, while the velocities and the electromagnetic fields converge to the equilibrium states with weaker norms than <alternatives><inline-graphic xlink:href="ark:/27927/pgj28jbmg31" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />‖.‖Hs-1</alternatives>. This phenomenon on the charge transport shows the essential difference between the unipolar Navier-Stokes-Maxwell and the bipolar Navier-Stokes-Maxwell system.