The generalized Caffarelli-Kohn-Nirenberg Theorem for the hyperdissipative Navier-Stokes system

TL;DR

This paper extends the regularity theory of the Caffarelli-Kohn-Nirenberg theorem to the hyperdissipative Navier-Stokes equations by introducing suitable weak solutions.

Contribution

It generalizes the classical regularity results to a broader class of hyperdissipative Navier-Stokes systems with a new notion of suitable weak solutions.

Findings

Extended regularity theory to hyperdissipative Navier-Stokes equations

Introduced a new notion of suitable weak solutions

Achieved a generalized Caffarelli-Kohn-Nirenberg theorem

Abstract

We introduce a notion of suitable weak solution of the hyperdissipative Navier-Stokes equations and we achieve a corresponding extension of the regularity theory of Caffarelli-Kohn-Nirenberg.