PreprintarXiv licencearXiv
Nonlinear stability of the Guderley imploding shock wave in radial symmetry
Abstract
We prove nonlinear stability of the Guderley imploding shock under radial perturbations for the three-dimensional compressible Euler equations in the adiabatic range 1<γ≤5/3. The perturbed solutions develop an asymptotically self-similar implosion in finite time. Our result allows perturbations with small, nonzero constant pressure in the quiescent region ahead of the shock. The proof combines weighted L∞ estimates along characteristics with a computer-assisted proof of stability inequalities for the Guderley profile.
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BibTeX
@misc{cialdea2026nonlinear,
title = {{Nonlinear stability of the Guderley imploding shock wave in radial symmetry}},
author = {Giorgio Cialdea},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01690},
eprint = {2610.01690},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01690},
}
RIS
TY - UNPB
TI - Nonlinear stability of the Guderley imploding shock wave in radial symmetry
AU - Giorgio Cialdea
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01690
UR - https://arxiv.org/abs/2610.01690
AB - We prove nonlinear stability of the Guderley imploding shock under radial perturbations for the three-dimensional compressible Euler equations in the adiabatic range 1<γ≤5/3. The perturbed solutions develop an asymptotically self-similar implosion in finite time. Our result allows perturbations with small, nonzero constant pressure in the quiescent region ahead of the shock. The proof combines weighted L^∞ estimates along characteristics with a computer-assisted proof of stability inequalities for the Guderley profile.
ER -