A Weighted Regularity Criterion for Suitable Weak Solutions of Incompressible Non-Newtonian Fluids

TL;DR

This paper introduces a new regularity criterion for solutions of incompressible non-Newtonian fluid equations, utilizing weighted gradient norms and the Caffarelli--Kohn--Nirenberg inequality to improve understanding of solution smoothness.

Contribution

It proposes a novel weighted regularity criterion for weak solutions of non-Newtonian fluids, extending classical criteria with weighted gradient conditions.

Findings

Established a new regularity criterion based on weighted gradients.

Connected the criterion with the Caffarelli--Kohn--Nirenberg inequality.

Enhanced criteria for solution regularity in non-Newtonian fluid models.

Abstract

It establishes a regularity criterion for non-Newtonian fluids in $\mathbb{R}^3$ in terms of the weighted gradient of the velocity field, based on the Caffarelli--Kohn--Nirenberg inequality.