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arXiv · 2609.36567

Shock profiles for the Navier--Stokes--Fourier--Poisson system under the Boltzmann relation

Renjun Duan·Rui Li
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Abstract

The one-dimensional compressible Navier--Stokes--Fourier--Poisson system under the Boltzmann relation is studied for the existence of small-amplitude viscous shock profiles connecting the Rankine--Hugoniot states of the quasineutral Euler system with effective pressure $P_{\mathrm{eff}}=ρ(θ+1)$. This profile is unique up to translation, of Lax type, and orbitally stable in time without a zero-mass assumption on the perturbation. The proof is based on a center-manifold reduction of the traveling-wave ODE and on the method of $a$-contraction with shifts, together with a relative-entropy functional augmented by electric energy and a sharp estimate of the viscous flux associated with $P_{\mathrm{eff}}$.

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Renjun Duan, Rui Li. 2026-09-29. Shock profiles for the Navier--Stokes--Fourier--Poisson system under the Boltzmann relation. https://arxiv.org/abs/2609.36567

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