Whether the 3D incompressible Euler and Navier-Stokes equations can develop a finite time singularity from smooth initial data is one of the most challenging problems in nonlinear PDEs. In an effort to provide a rigorous proof of the potential Euler singularity revealed by Luo-Hou's computation, we develop a novel method of analysis and prove that the original De Gregorio model and the Hou-Lou model develop a finite time singularity from smooth initial data. Using this framework and some techniques from Elgindi's recent work on the Euler singularity, we prove the finite time blowup of the 2D Boussinesq and 3D Euler equations with $C^{1,\alpha}$ initial velocity and boundary. Further, we present some new numerical evidence that the 3D incompressible Euler and Navier-Stokes equations with smooth initial data develop potentially singular behavior at the origin, which is quite different from the Hou-Luo scenario. Our study shows that the potentially singular solution of the 3D Navier-Stokes equations enjoys nearly self-similar scaling properties and the maximum vorticity has increased by a factor of $10^7$ relative to its initial maximum vorticity.
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