Year: 2026
Type: preprint
Abstract: We prove nonlinear stability of the Guderley imploding shock under radial perturbations for the three-dimensional compressible Euler equations in the adiabatic range $1<γ\leq\frac{5}{3}$. 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 $L^\infty$ estimates along characteristics with a computer-assisted proof of stability inequalities for the Guderley profile.
Source: arXiv (Cornell University)
Author: Cialdea, Giorgio
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7216245612