发表机构
School of Mathematics and Statistics, Nantong University; School of Mathematical Sciences, South China Normal University（南通大学数学与统计学院; 华南师范大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明一维完全可压缩Navier--Stokes--Poisson方程小振幅激波剖面存在唯一且渐近稳定，通过中心流形定理与积分系统能量估计实现。
AI 中文摘要
本文研究了一维完全可压缩Navier--Stokes--Poisson方程行波激波的存在性与渐近稳定性，该方程描述了自洽静电场中粘性导热离子的运动。我们首先利用中心流形定理证明了小振幅光滑激波剖面的存在性与唯一性，然后建立了其在适当小的光滑扰动下的大时间渐近稳定性。证明基于对由完全可压缩Navier--Stokes--Poisson方程导出的特殊构造的积分系统进行能量估计。为完成该估计，我们引入了适当的反导数变量，这些变量融合了自洽静电势和热传导的影响，从而将原始系统改写为耗散积分系统。随后的能量估计通过仔细处理诱导的耦合项得以完成。
英文摘要
This paper studies the existence and asymptotic stability of traveling shock waves for the one-dimensional full compressible Navier--Stokes--Poisson equations, which model viscous heat-conducting ions in a self-consistent electrostatic field. We first prove the existence and uniqueness of a smooth shock profile of small amplitude by the center manifold theorem, and then establish its large-time asymptotic stability under suitably small smooth perturbations. The proof is based on an energy estimate for a specially constructed integrated system derived from the full compressible Navier--Stokes--Poisson equations. To carry out this estimate, we introduce suitable anti-derivative variables that incorporate the effects of the self-consistent electrostatic potential and heat conduction, thereby reformulating the original system as a dissipative integrated one. The subsequent energy estimates are completed by carefully handling the induced couplings.
