Remarks on the three-dimensional Navier-Stokes equations with Lions' exponent forced by space-time white noise

We study the three-dimensional Navier-Stokes equations forced by space-time white noise and diffused via the fractional Laplacian with Lions’ exponent so that it is precisely the energy-critical case. We prove its global solution theory following the approach of Hairer and Rosati (2024, Annals of PDE, $\mathbf{\text{10}}$, pp. 1–46).