  Whether the 3D incompressible Euler equations can develop a finite time
singularity from smooth initial data is one of the most challenging problems in
nonlinear PDEs. In this paper, we present some new numerical evidence that the
3D axisymmetric incompressible Euler equations with smooth initial data of
finite energy develop a potential finite time singularity at the origin. This
potential singularity is different from the blow-up scenario revealed by
Luo-Hou in \cite{luo2014potentially,luo2014toward}, which occurs on the
boundary. Our initial condition has a simple form and shares several attractive
features of a more sophisticated initial condition constructed by Hou-Huang in
\cite{Hou-Huang-2021,Hou-Huang-2022}. One important difference between these
two blow-up scenarios is that the solution for our initial data has a one-scale
structure instead of a two-scale structure reported in
\cite{Hou-Huang-2021,Hou-Huang-2022}. More importantly, the solution seems to
develop nearly self-similar scaling properties that are compatible with those
of the 3D Navier-Stokes equations. We will present numerical evidence that the
3D Euler equations seem to develop a potential finite time singularity.
Moreover, the nearly self-similar profile seems to be very stable to the small
perturbation of the initial data.
