Convergence rate of solutions toward stationary solutions to the bipolar Navier-Stokes-Poisson equations in a half line
1 Department of Mathematics, Hubei University of Science and Technology, Xianning, 437100, P.R. China
2 Department of Mathematics, Shanghai Normal University, Shanghai, 200234, P.R. China
Boundary Value Problems 2013, 2013:124 doi:10.1186/1687-2770-2013-124Published: 14 May 2013
In this paper, we show the convergence rate of a solution toward the stationary solution to the initial boundary value problem for the one-dimensional bipolar compressible Navier-Stokes-Poisson equations. For the supersonic flow at spatial infinity, if an initial perturbation decays with the algebraic or the exponential rate in the spatial asymptotic point, the solution converges to the corresponding stationary solution with the same rate in time as time tends to infinity. For the transonic flow at spatial infinity, the solution converges to the stationary solution in time with the lower rate than that of the initial perturbation in the spatial. These results are proved by the weighted energy method.
MSC: 35M31, 35Q35.