Finite-time blowup conjecture for the Navier–Stokes strain equation without advection

Let $S$ be a mild solution of the Navier–Stokes strain equation without advection, with $S otag\in C\left([0,T_{max});L^2_{st}\right)$, where $L^2_{st}$ denotes the space of square-integrable strain fields. Finite-time blowup conjecture. There \exists such a solution with finite maximal time $T_{max}<+\infty$ satisfying

$$\lim_{t\to T_{\max}}\|S(\cdot,t)\|_{L^2}=+\infty.$$

The surrounding discussion presents this as a conjectural prediction based on the finite-time blowup known for the strain self-amplification model and the anticipated greater singularity of the case $\mu=1$; no proof or disproof is supplied.