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On the Well-Posedness of Periodic Strong Transonic Shocks in Divergent Nozzles
Abstract
This paper studies the C1 existence and dynamical stability of temporal periodic solutions involving strong transonic shocks for the quasi--one--dimensional full compressible Euler equations in diverging nozzles. We reveal the physical structural dissipation mechanism of strong transonic shocks hidden in the Rankine--Hugoniot conditions. This allows us to estimate the resonance at the shock boundary caused by the left acoustic waves in the subsonic downstream region. With this dissipation, we complete the proof by developing a fraction--step linearized iterative method.
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BibTeX
@misc{qu2026wellposedness,
title = {{On the Well-Posedness of Periodic Strong Transonic Shocks in Divergent Nozzles}},
author = {Peng Qu and Jiahui Wang and Huimin Yu and Xiaomin Zhang},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27852},
eprint = {2608.27852},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27852},
}
RIS
TY - UNPB
TI - On the Well-Posedness of Periodic Strong Transonic Shocks in Divergent Nozzles
AU - Peng Qu
AU - Jiahui Wang
AU - Huimin Yu
AU - Xiaomin Zhang
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.27852
UR - https://arxiv.org/abs/2608.27852
AB - This paper studies the C^1 existence and dynamical stability of temporal periodic solutions involving strong transonic shocks for the quasi--one--dimensional full compressible Euler equations in diverging nozzles. We reveal the physical structural dissipation mechanism of strong transonic shocks hidden in the Rankine--Hugoniot conditions. This allows us to estimate the resonance at the shock boundary caused by the left acoustic waves in the subsonic downstream region. With this dissipation, we complete the proof by developing a fraction--step linearized iterative method.
ER -