Mathematical analysis and multiscale derivation of a nonlinear predator-prey cross-diffusion--fluid system with two chemicals

TL;DR

This paper develops a mathematical framework for a predator-prey system with chemical interactions in a fluid, proving solution existence and deriving the model from kinetic-fluid theory, with computational validation.

Contribution

It introduces a novel multiscale derivation of a nonlinear predator-prey cross-diffusion-fluid system from kinetic-fluid theory, and proves the existence of weak solutions.

Findings

Existence of weak solutions established using Schauder fixed-point theory.

Model derived from multiscale kinetic-fluid approach.

Computational results demonstrate system behavior in 2D space.

Abstract

A nonlinear cross-diffusion--fluid system with chemical terms describing the dynamics of predator-prey living in a Newtonian fluid is proposed in this paper. The existence of a weak solution for the proposed macro-scale system is proved based on the Schauder fixed-point theory, a priori estimates, and compactness arguments. The proposed system is derived from the underlying description delivered by a kinetic-fluid theory model by a multiscale approach. Finally, we discuss the computational results for the proposed macro-scale system in two-dimensional space.