Low modes regularity criterion for a chemotaxis-Navier-Stokes system

TL;DR

This paper introduces a new regularity criterion for a 3D chemotaxis-Navier-Stokes system based on low modes of oxygen concentration and fluid velocity, improving upon previous criteria.

Contribution

It develops a novel low modes regularity criterion using a wavenumber splitting approach, advancing the understanding of regularity conditions for the system.

Findings

The criterion applies to a periodic domain.

It requires only low modes of key variables.

It improves existing regularity criteria.

Abstract

In this paper we study the regularity problem of a three dimensional chemotaxis-Navier-Stokes system on a periodic domain. A new regularity criterion in terms of only low modes of the oxygen concentration and the fluid velocity is obtained via a wavenumber splitting approach. The result improves many existing criteria in the literature.