Smooth and stable Euler implosions
Abstract
We construct a new class of self-similar implosion profiles for the multi-dimensional compressible Euler equations. These profiles are smooth, genuinely non-isentropic, radially/spherically symmetric, and have explicit (closed-form) similarity exponents. We prove that the exact Euler solution corresponding to the ground state implosion profile is stable to radially symmetric perturbations, as a solution to the full nonlinear compressible Euler equations, modulo a one-dimensional compatibility condition on the initial data. For perturbations of the Euler solution corresponding to the ground state implosion profile of a monatomic or diatomic gas, that do not obey any symmetry assumptions, we provide a complete characterization of the set of initial data that yield nonlinear stability.
Cite
@article{arxiv.2605.00808,
title = {Smooth and stable Euler implosions},
author = {Jiajie Chen and Steve Shkoller and Vlad Vicol},
journal= {arXiv preprint arXiv:2605.00808},
year = {2026}
}
Comments
153 pages, 6 figures