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Mathematics > Analysis of PDEs

arXiv:2509.13226 (math)
[Submitted on 16 Sep 2025 (v1), last revised 6 Oct 2025 (this version, v2)]

Title:Vorticity blow-up for the 3D incompressible Euler equations

Authors:Wenjie Deng, Song Jiang, Minling Li, Zhaonan Luo
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Abstract:In this paper, we study the finite-time blow-up for classical solutions of the 3D incompressible Euler equations with low-regularity initial vorticity. Applying the self-similar method and stability analysis of the self-similar system in critical Sobolev space, we prove that the vorticity of the axi-symmetric 3D Euler equations develops a finite-time singularity with certain scaling indices. Furthermore, we investigate the time integrability of the solutions. The proof is based on the new observations for the null structure of the transport term, and the parameter stability of the fundamental self-similar models.
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:2509.13226 [math.AP]
  (or arXiv:2509.13226v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2509.13226

Submission history

From: Wenjie Deng [view email]
[v1] Tue, 16 Sep 2025 16:37:01 UTC (76 KB)
[v2] Mon, 6 Oct 2025 09:14:10 UTC (76 KB)
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