The 3D incompressible Navier-Stokes equations with partial hyperdissipation

The three-dimensional incompressible Navier-Stokes equations with the hyperdisipation (-Delta)(gamma) always possess global smooth solutions when gamma >= 5/4 Tao[6] and Barbato, Morandin and Romito [1] made logarithmic reductions in the dissipation and still obtained the global regularity. This paper makes a different type of reduction in the dissipation and proves the global existence and uniqueness in the H-1-functional setting