Self-improving bounds for the Navier-Stokes equations

TL;DR

This paper extends blow-up criteria for Navier-Stokes solutions into negative regularity Besov spaces, enabling better understanding of solution regularity near critical thresholds.

Contribution

It introduces a method to convert a priori bounds in negative Besov spaces into bounds in positive regularity, extending existing blow-up criteria.

Findings

Extended blow-up criterion to negative Besov regularity near -1

Provided a new approach to relate negative and positive regularity bounds

Enhanced understanding of solution regularity thresholds for Navier-Stokes

Abstract

We consider regular solutions to the Navier-Stokes equation and provide an extension to the Escauriaza-Seregin-Sverak blow-up criterion in the negative regularity Besov scale, with regularity arbitrarly close to -1. Our results rely on turning a priori bounds for the solution in negative Besov spaces into bounds in the positive regularity scale.