The initial value problem (IVP) for the one-dimensional isentropic compressible Navier-Stokes-Poisson (CNSP) system is considered in this paper. For the variables, the electric field and the velocity, under the Lagrange coordinate, we establish the global existence and uniqueness of the classical solutions to this IVP problem. Then we prove by the method of complex analysis, that the solutions to this system converge to those of the corresponding linearized system in the L2 norm as time tends to infinity. In addition, we show, using Green’s function, that the solutions to this system are close to a diffusion profile, pointwisely, as time goes to infinity.
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