双极Navier-Stokes-Poisson方程整体解的存在性

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

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.