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

Abstract

We study exactly self-similar blow-up profiles for the generalized De Gregorio model for the three-dimensional Euler equation: We show that for any such that 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 Elgindi and Jeong (2020 Arch. Ration. Mech. Anal. 235 1763–817) by removing the restriction and Chen et al (2021 Commun. Pure Appl. Math. 74 1282–350), which only deals with asymptotically self-similar blow-ups.