Stability of stationary solutions to the inflow problem for the two-fluid non-isentropic Navier-Stokes-Poisson system
Stability of stationary solutions to the inflow problem for the two-fluid non-isentropic Navier-Stokes-Poisson system
复制标题
二流体非等熵纳维-斯托克斯-泊松系统流入问题平稳解的稳定性
DOI：
10.1016/j.jde.2018.03.016
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发表时间：
2018
影响因子：
2.4
通讯作者：
Wang Teng
中科院分区：
文献类型：
--
作者：
Hong Hakho;Shi Xiaoding（施小丁）;Wang Teng
在本文中，我们研究了半线(0,∞)内二流体非等熵Navier-Stokes-Poisson系统初始边值问题解的渐近行为。我们考虑一个流入问题，其中气体通过一般气体（包括理想多方气体）的边界进入该区域。由于准中性假设和大时间行为中不存在电场，我们借助中心流形理论证明了平稳解的存在性，并严格证明了Navier-Stokes-Poisson系统相应的初始边值问题在小扰动下平稳解的稳定性定理。请注意，这是纳维-斯托克斯-泊松系统流入问题非线性波稳定性的第一个结果。
In this paper, we study the asymptotic behavior of solution to the initial boundary value problem for the two-fluid non-isentropic Navier–Stokes–Poisson system in a half line (0,∞). We consider an inflow problem where the gas enter into the region through the boundary for general gases including ideal polytropic gas. On account of the quasineutral assumption and the absence of the electric field for the large time behavior, we show the existence of the stationary solutions with the aid of the center manifold theory, and then we give the rigorous proof of the stability theorem on the stationary solutions under small perturbations for the corresponding initial boundary value problem of the Navier–Stokes–Poisson system. Note that it is the first result for the stability of nonlinear waves on the inflow problem of the Navier–Stokes–Poisson system.