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Asymptotic stability of stationary solutions to the compressible bipolar Navier–Stokes–Poisson equations
Author(s) -
Cai Hong,
Tan Zhong
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4320
Subject(s) - mathematics , uniqueness , mathematical analysis , initial value problem , compressibility , energy method , nonlinear system , perturbation (astronomy) , stationary state , poisson distribution , constant (computer programming) , exponential stability , cauchy problem , physics , mechanics , quantum mechanics , statistics , computer science , programming language
In this paper, we consider the compressible bipolar Navier–Stokes–Poisson equations with a non‐flat doping profile in three‐dimensional space. The existence and uniqueness of the non‐constant stationary solutions are established when the doping profile is a small perturbation of a positive constant state. Then under the smallness assumption of the initial perturbation, we show the global existence of smooth solutions to the Cauchy problem near the stationary state. Finally, the convergence rates are obtained by combining the energy estimates for the nonlinear system and the L 2 ‐decay estimates for the linearized equations. Copyright © 2017 John Wiley & Sons, Ltd.