# Local energy bounds and $\epsilon$-regularity criteria for the 3D Navier-Stokes system

## TL;DR

This paper introduces new local energy bounds for the 3D Navier-Stokes equations, improving epsilon-regularity criteria by analyzing pressure oscillations through fractional Sobolev spaces.

## Contribution

It presents novel local energy bounds and epsilon-regularity criteria for the 3D Navier-Stokes system, emphasizing the pressure's fractional Sobolev space analysis.

## Key findings

- Enhanced epsilon-regularity criteria for Navier-Stokes
- Pressure oscillation characterization via fractional Sobolev spaces
- Improved understanding of local energy bounds in fluid dynamics

## Abstract

The system of three dimensional Navier-Stokes equations is considered. We obtain some new local energy bounds that enable us to improve several $\epsilon$-regularity criteria. They key idea here is to view the `head pressure' as a signed distribution belonging to certain fractional Sobolev space of negative order. This allows us to capture the oscillation of the pressure in our criteria.