  In this paper, we consider a model equation for the Navier--Stokes strain
equation. This model equation has the same identity for enstrophy growth and a
number of the same regularity criteria as the full Navier-Stokes strain
equation, and is also an evolution equation on the same constraint space. We
prove finite-time blowup for this model equation, which shows that the identity
for enstrophy growth and the strain constraint space are not sufficient on
their own to guarantee global regularity for Navier-Stokes. The mechanism for
the finite-time blowup of this model equation is the self-amplification of
strain, which is consistent with recent research suggesting that strain
self-amplification, not vortex stretching, is the main mechanism behind the
turbulent energy cascade. Because the strain self-amplification model equation
is obtained by dropping certain terms from the full Navier-Stokes strain
equation, we will also prove a conditional blowup result for the full
Navier-Stokes equation involving a perturbative condition on the terms
neglected in the model equation.
