PreprintCC BY 4.0arXiv
Shock solutions of a 3D spherical piston problem for the compressible Euler equations
Abstract
This paper establishes the global well-posedness of shock solutions for a 3D spherical piston problem to the compressible Euler equations. The main mathematical challenges are the nonlinear coupling between the free shock boundary and the moving piston, alongside potential gradient catastrophes induced by spherical geometric source terms. To overcome these difficulties, we reformulate the problem using Riemann invariants and introduce a tailored directional derivative along the unperturbed piston trajectory. Then we can extend the local solution to construct a global piecewise smooth solution including a single shock under some moderate assumptions.
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BibTeX
@misc{zhou2026shock,
title = {{Shock solutions of a 3D spherical piston problem for the compressible Euler equations}},
author = {Pengfei Zhou and Huimin Yu and Xiaomin Zhang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08260},
eprint = {2611.08260},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08260},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Shock solutions of a 3D spherical piston problem for the compressible Euler equations
AU - Pengfei Zhou
AU - Huimin Yu
AU - Xiaomin Zhang
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08260
UR - https://arxiv.org/abs/2611.08260
AB - This paper establishes the global well-posedness of shock solutions for a 3D spherical piston problem to the compressible Euler equations. The main mathematical challenges are the nonlinear coupling between the free shock boundary and the moving piston, alongside potential gradient catastrophes induced by spherical geometric source terms. To overcome these difficulties, we reformulate the problem using Riemann invariants and introduce a tailored directional derivative along the unperturbed piston trajectory. Then we can extend the local solution to construct a global piecewise smooth solution including a single shock under some moderate assumptions.
ER -