Finite time singularities to the 3D incompressible Euler equations for solutions in $$C^{\infty}(\mathbb{R}^3 \setminus \{0\})\cap C^{1,α}\cap L^2$$

Abstract: We introduce a novel mechanism that reveals finite time singularities within the 1D De Gregorio model and the 3D incompressible Euler equations. Remarkably, we do not construct our blow up using self-similar coordinates, but build it from infinitely many regions with vorticity, separated by vortex-free regions in between. It yields solutions of the 3D incompressible Euler equations in $\mathbb{R}^3\times [-T,0]$ such that the velocity is in the space $$C^{{\infty}(\mathbb{R}³} \setminus {0})\cap C^{{1,\alpha}\cap} L<sup>2$$ for times $t\in (-T,0)$ and is not $C<sup>1$ at time 0.