Exactly self-similar blow-up of the generalized De Gregorio equation

2022/09/20 by Zheng Fan, Zheng, Fan · 1 citation
Mathematics · Physics and Astronomy · #35F25 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2209.09886

openalex publication_date 2022/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study exactly self-similar blow-up profiles fot the generalized De Gregorio model for the three-dimensional Euler equation: w_t + auw_x = u_xw, u_x = Hw We show that for any α∈ (0, 1) such that |aα| is sufficiently small, there is an exactly self-similar C^α solution that blows up in finite time. This simultaneously improves on the result in \citeElJe by removing the restriction 1/α∈ \mathbb Z and \citeEl-GhMa,ChHoHu, which only deals with asymptotically self-similar blow-ups.

Cited by

• Stability and Instability on the De Gregorio Modification of the Constantin-Lax-Majda model

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