We prove global existence of smooth solutions for a slightly supercritical hyperdissipative Navier–Stokes under the optimal condition on the correction to the dissipation. This proves a conjecture formulated by Tao.
"Global regularity for a slightly supercritical hyperdissipative Navier–Stokes system." Anal. PDE 7 (8) 2009 - 2027, 2014. https://doi.org/10.2140/apde.2014.7.2009