Whether the 3D incompressible Navier-Stokes equations can develop a finite time singularity from smooth initial data is one of the seven Clay Millennium Prize Problems. We first review our recent work in developing a rigorous computer assisted proof of the 3D Euler singularity with smooth initial data and boundary. We then present some numerical evidence that the 3D Navier-Stokes equations develop potentially singular behavior at the origin with maximum vorticity increased by a factor of $10^7$. This potentially singular behavior is induced by a potential finite time singularity of the 3D Euler equations. We have applied several blowup criteria to study this potentially singular behavior of the Navier-Stokes equations. Finally, we present some new numerical evidence that a generalized axisymmetric Navier-Stokes equation with time dependent fractional dimension develops a tornado like self-similar blowup with the maximum vorticity increased by a factor of $10^{21}$.