Global existence for an attraction-repulsion chemotaxis fluid model with logistic source

TL;DR

This paper proves the global existence of solutions for a chemotaxis-fluid model with logistic growth, involving cell-chemical interactions and fluid dynamics, in two and three-dimensional bounded domains.

Contribution

It establishes the existence of global mild solutions for the coupled chemotaxis-Navier-Stokes system with logistic source under small initial data.

Findings

Global mild solutions exist in 2D and 3D for small initial data.

The model captures cell proliferation, chemical interactions, and fluid transport.

Existence results are proved in bounded domains of RN.

Abstract

We consider an attraction-repulsion chemotaxis model coupled with the Navier-Stokes system. This model describes the interaction between a type of cells (e.g., bacteria), which proliferate following a logistic law, and two chemical signals produced by the cells themselves that degraded at a constant rate. Also, it is considered that the chemoattractant is consumed with a rate proportional to the amount of organisms. The cells and chemical substances are transported by a viscous incompressible fluid under the influence of a force due to the aggregation of cells. We prove the existence of global mild solutions in bounded domains of RN , N = 2, 3, for small initial data in Lp-spaces.