可压缩Navier-Stokes-Poisson方程波的稳定性

Plasma, e.g. dusty and the neon lights in the internal of star and so on, could simulate the transport of charged electrons and ions in the process of the mutual collision. These electrons and ions form the self-consistent electric potential. We usually use two-fluid Navier-Stokes-Poisson (NSP) equation to describe the dynamics of the charged particles in the collisional plasma under the influence of the self-consistent electric potential. This project is concerned with the stability of waves for one-dimensional non-isentropic one-fluid and two-fluid Navier-Stokes-Poisson equation. For the one-fluid NSP equation, the applicant expects to obtain the stability of the contact discontinuity for the Cauchy problem in the case where the electron background density satisfies an analogue of the Boltzmann relation. For the two-fluid NSP equation, the applicant expects to respectively obtain the stability of rarefaction wave and composite wave (the superposition of rarefaction wave and contact discontinuity ) for the Cauchy problem in the case where the electron density and ion density satisfy the quasineutral assumption.

尘埃, 恒星内部的霓虹灯等等离子体在相互碰撞的过程中会产生带电的电子和离子。这些电子和离子会形成自一致的电势。在自一致电势的影响下, 我们往往用双极的Navier-Stokes-Poisson方程来描述带电物质的运动。本项目分别考虑一维非等熵单极和双极NSP方程波的稳定性。假设电子的背景密度满足类似的Boltzmann关系时, 申请人期望获得单极NSP方程柯西问题接触间断的稳定性。当电子的密度和离子的密度满足拟中性假设时, 申请人期望分别获得双极NSP方程柯西问题稀疏波和复合波(稀疏波和接触间断的复合)的稳定性。

本项目主要研究了非等熵的Navier-Stokes-Poisson方程复合波(稀疏波和接触间断波的复合)的稳定性、非等熵微极流模型边界层解的稳定性及其收敛率、平面Magnetohydrodynamics模型复合波(亚音速边界层，稀疏波和接触间断波)的稳定性以及 Navier-Stokes/Allen-Cahn方程复合波(稀疏波和接触间断波的复合)的稳定性等相关问题。以上研究的四种模型都可以看成Navier-Stokes方程的一种推广。