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Periodic dynamics of transonic shocks in Euler-Poisson flows
Abstract
This paper studies the existence and dynamical stability of time-periodic transonic shock solutions to the one-dimensional Euler--Poisson equations under periodic boundary perturbations. The analysis relies on two key mechanisms: the structural dissipation induced by the transonic shock and the stabilization effect of the positive electric field on the shock position. Using a reformulation of the Rankine-Hugoniot conditions and uniform estimates on the flow and shock perturbations, we establish the existence of a time-periodic transonic shock solution. We further prove its dynamical stability under small perturbations of the initial data.
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BibTeX
@misc{qu2026periodic,
title = {{Periodic dynamics of transonic shocks in Euler-Poisson flows}},
author = {Peng Qu and Jiahui Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35402},
eprint = {2610.35402},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35402},
}
RIS
TY - UNPB
TI - Periodic dynamics of transonic shocks in Euler-Poisson flows
AU - Peng Qu
AU - Jiahui Wang
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35402
UR - https://arxiv.org/abs/2610.35402
AB - This paper studies the existence and dynamical stability of time-periodic transonic shock solutions to the one-dimensional Euler--Poisson equations under periodic boundary perturbations. The analysis relies on two key mechanisms: the structural dissipation induced by the transonic shock and the stabilization effect of the positive electric field on the shock position. Using a reformulation of the Rankine-Hugoniot conditions and uniform estimates on the flow and shock perturbations, we establish the existence of a time-periodic transonic shock solution. We further prove its dynamical stability under small perturbations of the initial data.
ER -