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Shock profiles for the Navier--Stokes--Fourier--Poisson system under the Boltzmann relation
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 Peff=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 Peff.
Related
- Existence and stability of shock profiles for a one-dimensional full compressible Navier--Stokes--Poisson equations
- Existence and uniqueness of viscous-dispersive shock profiles for the Navier-Stokes-Fourier-Korteweg system
- Asymptotic profiles for solutions to the incompressible Navier-Stokes equations in the critical Fourier-Herz spaces
- Global Stability and Energy Growth in the Sheared Vlasov--Poisson--Boltzmann System
- Hydrodynamic limits for the Boltzmann-Fermi-Dirac equation: Acoustic and Stokes-Fourier
BibTeX
@misc{duan2026shock,
title = {{Shock profiles for the Navier--Stokes--Fourier--Poisson system under the Boltzmann relation}},
author = {Renjun Duan and Rui Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36567},
eprint = {2609.36567},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36567},
}
RIS
TY - UNPB
TI - Shock profiles for the Navier--Stokes--Fourier--Poisson system under the Boltzmann relation
AU - Renjun Duan
AU - Rui Li
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.36567
UR - https://arxiv.org/abs/2609.36567
AB - 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_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_eff.
ER -