Convergence rates of solutions for a two-species chemotaxis-Navier-Stokes sytstem with competitive kinetics

TL;DR

This paper investigates how quickly solutions to a two-species chemotaxis-Navier-Stokes system with competitive interactions approach equilibrium, providing explicit convergence rates based on model parameters and space dimension.

Contribution

It establishes convergence rates for solutions to a chemotaxis-Navier-Stokes system with competitive kinetics, highlighting cases where rates depend on the Poincare constant.

Findings

Convergence rates are derived for the system's solutions.

Most rates depend on model parameters and space dimension.

One case expresses fluid convergence rate via Poincare constant.

Abstract

In this paper, we study the rates of convergence of supposedly given global bounded classical solutions to a two-species chemotaxis-Navier-Stokes system with Lotka-Volterra competitive kinetics. Except in one case where the rate of convergence for the fluid component is expressed in terms of the Poincare constant and the model parameters, all other rates of convergence are shown to be expressible only in terms of the model parameters and the underlying space dimension.