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arXiv · 2509.13226

Non-implosion mechanism of 3D incompessible Euler equations

Wenjie Deng·Song Jiang·Minling Li·Zhaonan Luo
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Abstract

This paper studies the non-implosion mechanism for the 3D incompressible Euler equations. We prove that vorticity blows up in finite time, whereas the $L^p_T L^\infty_{loc}$ $(p\in[1,\infty))$ norm of the velocity field remains bounded. Moreover, under an appropriate assumption on the scaling index, the exponent $p$ can be taken to be infinite. The proof is based on the introduction of a refined framework, the new observations for the null structure of transport term, and stability analysis of the self-similar model.

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Wenjie Deng, Song Jiang, Minling Li, Zhaonan Luo. 2025-09-16. Non-implosion mechanism of 3D incompessible Euler equations. https://arxiv.org/abs/2509.13226

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