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arXiv · 2605.00808

Smooth and stable Euler implosions

Jiajie Chen·Steve Shkoller·Vlad Vicol
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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.

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Jiajie Chen, Steve Shkoller, Vlad Vicol. 2026-05-01. Smooth and stable Euler implosions. https://arxiv.org/abs/2605.00808

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