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 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.
Global regularity for a logarithmically supercritical hyperdissipative dyadic equation / Barbato, David; Morandin, Francesco; Romito, Marco. - In: DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 1548-159X. - 11:1(2014), pp. 39-52. [10.4310/DPDE.2014.v11.n1.a2]