Existence and stability of shock profiles for a one-dimensional full compressible Navier--Stokes--Poisson equations

Yeping Li; Yuan Yuan

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arXiv · 2610.04257

Existence and stability of shock profiles for a one-dimensional full compressible Navier--Stokes--Poisson equations

Yeping Li·Yuan Yuan

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Abstract

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.

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Yeping Li, Yuan Yuan. 2026-10-03. Existence and stability of shock profiles for a one-dimensional full compressible Navier--Stokes--Poisson equations. https://arxiv.org/abs/2610.04257

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