# Global existence and asymptotic behavior of classical solutions for a 3D two-species chemotaxis-Stokes system with competitive kinetics

## TL;DR

This paper proves the global existence, boundedness, and stabilization of solutions for a three-dimensional two-species chemotaxis-Stokes system with competitive kinetics, extending previous 2D results to 3D.

## Contribution

It provides the first comprehensive results on global solutions and their asymptotic behavior for the 3D coupled chemotaxis-fluid system with competition.

## Key findings

- Global existence of solutions in 3D
- Solutions are bounded over time
- Solutions stabilize asymptotically

## Abstract

This paper considers the two-species chemotaxis-Stokes system with competitive kinetics under homogeneous Neumann boundary conditions in a three-dimensional bounded domain with smooth boundary. Both chemotaxis-fluid systems and two-species chemotaxis systems with competitive terms are studied by many mathematicians. However, there has not been rich results on coupled two-species-fluid systems. Recently, global existence and asymptotic stability in this problem with convection term in the fluid equation of the above system were established in the 2-dimensional case. The purpose of this paper is to give results for global existence, boundedness and stabilization of solutions to this system in the 3-dimensional case.