Global regularity for a slightly supercritical hyperdissipative Navier-Stokes system. (English) Zbl 1309.76053

Barbato, David; Morandin, Francesco; Romito, Marco

Anal. PDE 7, No. 8, 2009-2027 (2014).

Summary: 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 T. Tao [Anal. PDE 2, No. 3, 361–366 (2009; Zbl 1190.35177)].

MSC:

76D03	Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05	Navier-Stokes equations for incompressible viscous fluids
35Q30	Navier-Stokes equations
35Q35	PDEs in connection with fluid mechanics

Keywords:

Navier-Stokes; dyadic model; global existence; slightly supercritical Navier-Stokes