Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (4): 1098-1116.doi: 10.1016/S0252-9602(16)30058-3

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THE STABILITY OF STATIONARY SOLUTION FOR OUTFLOW PROBLEM ON THE NAVIER-STOKES-POISSON SYSTEM

Mina JIANG1, Suhua LAI1, Haiyan YIN2, Changjiang ZHU3   

  1. 1 School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China;
    2 School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China;
    3 School of Mathematics, South China University of Technology, Guangzhou 510641, China
  • Received:2015-07-24 Revised:2016-01-24 Online:2016-08-25 Published:2016-08-25
  • Contact: Changjiang ZHU,E-mail:machjzhu@scut.edu.cn E-mail:machjzhu@scut.edu.cn
  • Supported by:

    The research was supported by the National Natural Science Foundation of China (11331005, 11471134), the Program for Changjiang Scholars and Innovative Research Team in University (IRT13066), and the Scientific Research Funds of Huaqiao University (15BS201, 15BS309).

Abstract:

In this article, we are concerned with the stability of stationary solution for outflow problem on the Navier-Stokes-Poisson system. We obtain the unique existence and the asymptotic stability of stationary solution. Moreover, the convergence rate of solution towards stationary solution is obtained. Precisely, if an initial perturbation decays with the algebraic or the exponential rate in space, the solution converges to the corresponding stationary solution as time tends to infinity with the algebraic or the exponential rate in time. The proof is based on the weighted energy method by taking into account the effect of the self-consistent electric field on the viscous compressible fluid.

Key words: Navier-Stokes-Poisson system, stationary solution, outflow problem, convergence rate, weighted energy method

CLC Number: 

  • 35B35
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