Global regularity for a slightly supercritical hyperdissipative Navier-Stokes system

TL;DR

This paper proves the global existence of smooth solutions for a slightly supercritical hyperdissipative Navier-Stokes system, confirming a conjecture by Tao and advancing understanding of supercritical fluid dynamics.

Contribution

It establishes the optimal condition for dissipation correction ensuring global regularity, solving a conjecture posed by Tao in 2009.

Findings

Global smooth solutions exist under optimal dissipation conditions

Confirms Tao's conjecture on supercritical Navier-Stokes systems

Advances theoretical understanding of hyperdissipative fluid models

Abstract

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 Tao [Tao2009].