数学物理学报 ›› 2014, Vol. 34 ›› Issue (4): 960-976.

• 论文 • 上一篇    下一篇

双极Navier-Stokes-Poisson方程整体解的存在性

刘健|连汝续|钱茂福   

  1. 衢州学院教师教育学院 浙江 衢州 324000;华北水利水电学院数学与信息学院 |郑州 450011;首都师范大学数学科学学院 北京 100048
  • 收稿日期:2012-12-08 修回日期:2013-11-30 出版日期:2014-08-25 发布日期:2014-08-25
  • 基金资助:

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

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

摘要:

考虑粘性系数依赖于密度的一维可压缩双极Navier-Stokes-Poisson(NSP)方程的初边值问题. 首先对于一般初值证明了弱解的整体存在性, 其次证明了真空状态若存在必在有限时间内消失. 进一步, 在真空消失之后, 整体弱解变成强解并且以指数形式收敛到非真空平衡态. 该文把文献[14]的结果推广到NSP的情形.

关键词: 双极Navier-Stokes-Poisson方程, 整体弱解, 真空消失, 大时间行为

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

中图分类号: 

  • 35Q35