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 $C^{ \infty}(\mathbb{ R}^3 \setminus \{ 0\})\cap C^{ 1,\alpha}\cap L^2$ for times $t\in (-T,0)$ and is not $C^1$ at time 0.
Categories: math.AP