The 3D incompressible Navier–Stokes equations with partial hyperdissipation

Wanrong Yang, Quansen Jiu and Jiahong Wu

Mathematische Nachrichten, 2019, vol. 292, issue 8, 1823-1836

Abstract: 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.

Date: 2019
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