December 1, 2025

A convergent time scheme for a chemotaxis-fluids model with potential consumption

Key Points

Global weak solutions were established in a chemotaxis-fluids model with consumption, indicating significant advancements in the field.
The study provides a time discretization scheme ensuring weak solutions remain uniformly bounded over time.
Assessment of the Keller–Segel–Navier–Stokes system reveals challenges due to fluid flow and potential consumption dynamics.
The findings could enhance mathematical modeling approaches to biological systems governed by chemotaxis.

Abstract

The present work deals with a Keller–Segel–Navier–Stokes system with potential consumption, under homogeneous Neumann boundary conditions for cell density and chemical signal, and Dirichlet type for the velocity field, over a bounded three-dimensional domain. The paper aims to develop a time discretization scheme converging to weak solutions of the system, which are uniformly bounded at infinite time. While global existence results are already known for simplified cases, either in absence of fluid flow or for linear consumption, the existence of global weak solutions for the fully coupled system with potential consumption has remained as an open problem.

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Cite This Study

Barbosa et al. (Mon,) studied this question.

synapsesocial.com/papers/69402c532d562116f2902bd8 https://doi.org/https://doi.org/10.1051/m2an/2025083/pdf

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