Epsilon regularity for the Navier-Stokes equations via weak-strong uniqueness

TL;DR

This paper presents a new, concise proof of an epsilon regularity criterion for the Navier-Stokes equations, leveraging weak-strong uniqueness and inspired by stationary system approaches.

Contribution

It introduces a novel proof technique for epsilon regularity in Navier-Stokes using weak-strong uniqueness, extending prior stationary system methods.

Findings

Provides a simplified proof of epsilon regularity criterion

Utilizes weak-strong uniqueness for non-zero boundary conditions

Inspired by stationary system approaches

Abstract

We give a new concise proof of a certain one-scale epsilon regularity criterion using weak-strong uniqueness for solutions of the Navier-Stokes equations with non-zero boundary conditions. It is inspired by an analogous approach for the stationary system due to Struwe.