Time discretization of a semi-discrete scheme for 3D Chemotaxis-Navier-Stokes system driven by transport noise

TL;DR

This paper analyzes the convergence of a semi-implicit Euler time discretization scheme for a complex 3D chemotaxis-Navier-Stokes system influenced by transport noise, combining biological modeling with stochastic fluid dynamics.

Contribution

It introduces a novel semi-implicit Euler scheme for a coupled chemotaxis-Navier-Stokes model with transport noise and establishes its well-posedness and uniform estimates.

Findings

Proved convergence of the proposed numerical scheme.

Established uniform bounds for discrete variables.

Validated the scheme's effectiveness for 3D models.

Abstract

This work is devoted to the convergence of a time-discrete numerical scheme of a semi-discretization model arising from biology, consisting of a chemotaxis equation coupled with a Galerkin approximation of Navier-Stokes system driven by transport noise in a three-dimensional bounded and convex domain. We propose a semi-implicit Euler numerical scheme approximating the infinite dimensional model, for which we study the well-posedness and derive some uniform estimates for the discrete variables