Asymptotic stability of stationary solutions to the compressible bipolar Navier–Stokes–Poisson equations |
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Authors: | Hong Cai Zhong Tan |
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Institution: | 1. School of Mathematical Sciences, Xiamen University, Xiamen, Fujian, China;2. School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling & High performance Scientific Computing, Xiamen University, Xiamen, Fujian, China |
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Abstract: | 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 L2‐decay estimates for the linearized equations. Copyright © 2017 John Wiley & Sons, Ltd. |
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Keywords: | bipolar Navier– Stokes– Poisson equations stationary solutions asymptotic stability |
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