Global regularity for a slightly supercritical hyperdissipative   Navier-Stokes system
  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 [Tao2009]. 
David Barbato, Francesco Morandin and Marco Romito
math.AP