condition $ \, \nabla \cdot \,
\pmb{u} = 0$, where $\pmb{u}$ is the velocity of the fluid, $p$ is the kinematic pressure, $\nu$ is the kinematic viscosity, and $\pmb{f}$ the external force. Taking the curl yields the vorticity formulation, $$\frac{\partial \pmb{\omega}}{\partial t} + (\pmb{u} \cdot \nabla) \pmb{\omega} =  \nu \triangle \pmb{\omega} + 
  (\pmb{\omega} \cdot \nabla) \pmb{u} +  \, \nabla \times \pmb{f}$$ where $\pmb{\omega}$ is the vorticity of the fluid, $\pmb{\omega} = \, \nabla \times \pmb{u} \, $. The left-hand side represents the transport of the vorticity by the velocity, the first term on the right-hand side generates the diffusion, and the second one is the vortex-stretching term; these are the three principal physical mechanisms in the system. Despite its apparent simplicity, the mathematical theory of the 3D NSE is fundamentally incomplete. In particular, since the pioneering work of J. Leray in the 1930s [@Le34], the question of whether a finite-time singularity can form in an initially regular (smooth) unforced flow is still open, and is one of the remaining *Millennium Prize Problems* put forth by the Clay Mathematics Institute (customarily referred to as ‘the NS regularity problem’). Note that–in this context–a temporal point $T^*$ is a *singularity* if the solution 