Global regularity for a logarithmically supercritical hyperdissipative   dyadic equation
  We prove global existence of smooth solutions for a slightly supercritical dyadic model. We consider a generalized version of the dyadic model introduced by Katz-Pavlovic [2005] and add a viscosity term with critical exponent and a supercritical correction. This model catches for the dyadic a conjecture that for Navier-Stokes equations was formulated by Tao [2009]. 
David Barbato, Francesco Morandin and Marco Romito
math.AP