Asymptotic stability of stationary solutions to the compressible bipolar Navier–Stokes–Poisson equations. (26th January 2017)

• Record Type: Journal Article
• Authors: Cai, Hong; Tan, Zhong
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 12(2017)
• Page Start: 4493
• Page End: 4513
• Publication Date: 2017-01-26
• Subjects: bipolar Navier–Stokes–Poisson equations -- stationary solutions -- asymptotic stability; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4320
• Languages: English
• ISSNs: 0170-4214

Abstract

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 L 2 ‐decay estimates for the linearized equations. Copyright © 2017 John Wiley & Sons, Ltd.