Global existence and temporal decay in Keller-Segel models coupled to fluid equations

TL;DR

This paper investigates the Keller-Segel model coupled with incompressible Navier-Stokes equations, establishing local and global existence of solutions, blow-up criteria, and decay estimates in 2D and 3D under certain initial data conditions.

Contribution

It provides new results on global existence, decay, and blow-up criteria for coupled Keller-Segel and fluid equations in both two and three dimensions.

Findings

Global existence and decay under small initial data

Blow-up criteria for oxygen concentration equations

Local existence of regular solutions in 2D and 3D

Abstract

We consider a Keller-Segel model coupled to the incompressible Navier-Stokes equations in spatial dimensions two and three. We establish the local existence of regular solutions and present some blow-up criteria for both cases that equations of oxygen concentration is of parabolic or hyperbolic type. We also prove global existence and decay estimate in time under the some smallness conditions of initial data.