The 3D incompressible Navier–Stokes equations with partial hyperdissipation

The three‐dimensional incompressible Navier–Stokes equations with the hyperdissipation (−Δ)γ always possess global smooth solutions when γ≥54. 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 H1‐functional setting.