Periodic dynamics of transonic shocks in Euler-Poisson flows

Peng Qu; Jiahui Wang

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arXiv · 2610.35402

Periodic dynamics of transonic shocks in Euler-Poisson flows

Peng Qu·Jiahui Wang

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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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Peng Qu, Jiahui Wang. 2026-10-26. Periodic dynamics of transonic shocks in Euler-Poisson flows. https://arxiv.org/abs/2610.35402

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