双极Navier-Stokes-Poisson方程整体解的存在性  

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

作　　者：刘健[1] 连汝续[2] 钱茂福[3] 

机构地区：[1]衢州学院教师教育学院,浙江衢州324000 [2]华北水利水电学院数学与信息学院,郑州450011 [3]首都师范大学数学科学学院,北京100048

出　　处：《数学物理学报（A辑）》2014年第4期960-976,共17页Acta Mathematica Scientia

基　　金：衢州学院博士启动基金(BSYJ201314);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.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 genera/ 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 tile non-vacuum equilibrium state exponentially in time. This extends the previous results for compressible NS [14] to NSP.

关 键 词：双极Navier-Stokes-Poisson方程 整体弱解 真空消失 大时间行为 

分 类 号：O175.2[理学—数学]