Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (4): 960-976.

• Articles • Previous Articles     Next Articles

Global Existence of Solution to Bipolar Navier-Stokes-Poisson System

 LIU Jian, LIAN Ru-Xu, QIAN Mao-Fu   

  1. College of Teacher Education, Quzhou University, Zhejiang Quzhou 324000; College of Mathematics and Information Science, North China University of Water Resources and Electric Power,    |Zhengzhou 450011; Department of Mathematics, Capital Normal University, Beijing 100048
  • Received:2012-12-08 Revised:2013-11-30 Online:2014-08-25 Published:2014-08-25
  • Supported by:

    衢州学院博士启动基金(BSYJ201314)和国家自然科学基金(11101145)资助

Abstract:

In this paper, we consider the initial boundary value problem (IBVP) for one-dimensional compressible bipolar Navier-Stokes-Poisson (BNSP) equations with density-dependent viscosities. First, it is proved that the weak solution for general initial data exists globally in time. Then, it is shown that vacuum state must vanish within finite time. Furthermore, after the vanishing of vacuum state, the global weak solution becomes a strong solution and tends to the non-vacuum equilibrium state exponentially in time. This extends the previous results for compressible NS [14] to NSP.

Key words: Bipolar Navier-Stokes-Poisson equation, Global weak solution, Vanishing of vacuum state, Large time behavior

CLC Number: 

  • 35Q35
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