Conditional estimates in three-dimensional chemotaxis-Stokes systems and application to a Keller-Segel-fluid model accounting for gradient-dependent flux limitation

TL;DR

This paper proves that flux limitation can prevent blow-up in a three-dimensional chemotaxis-Stokes system, ensuring global bounded solutions under optimal conditions, and establishes conditional bounds for fluid and gradient fields.

Contribution

It extends blow-up prevention results from fluid-free models to full chemotaxis-fluid systems, providing a condensed proof of global existence for broad initial data.

Findings

Flux limitation prevents blow-up in 3D chemotaxis-Stokes systems.

Global bounded solutions exist for a wide range of initial data.

Conditional bounds for fluid and taxis gradients are established.

Abstract

This manuscript deals with the three-dimensional version of a flux-limited Keller-Segel system coupled to the incompressible Stokes equations through transport and buoyancy. The main goal consists in verifying that within a certain parameter regime, known as being optimal therefor in some fluid-free simplification, a feature of blow-up prevention by suitably strong flux limitation persists also in the framework of the considered full chemotaxis-fluid system. To achieve this, as a secondary objective of possibly independent interest the manuscript separately establishes some conditional bounds for fluid fields and taxis gradients in a fairly general setting. The application thereof to the specific problem under consideration thereafter facilitates the derivation of a result on global existence of bounded classical solutions for widely arbitrary initial data actually, indeed within the entire and essentially optimal parameter range, through an argument which appears to be signficantly condensed when compared to reasonings pursued in previous related works.