On the existence and uniqueness of solution to a stochastic Chemotaxis-Navier-Stokes model

TL;DR

This paper proves the existence and uniqueness of a strong solution to a stochastic Chemotaxis-Navier-Stokes model, demonstrating key properties like non-negativity, mass conservation, and energy bounds in a two-dimensional setting.

Contribution

It establishes the first rigorous proof of existence and uniqueness for a stochastic Chemotaxis-Navier-Stokes system with detailed solution properties.

Findings

Existence of a unique strong solution is proven.

The solution maintains non-negativity and conserves mass.

Energy inequalities are satisfied by the solution.

Abstract

In this article, we study a mathematical system which models the dynamic of the collective behaviour of oxygen-driven swimming bacteria in an aquatic fluid flowing in a two dimensional bounded domain under stochastic perturbation. This model can be seen as a stochastic version of Chemotaxis-Navier-Stokes model. We prove the existence of a unique (probabilistic) strong solution. In addition, we establish some properties of the strong solution. More precisely, we prove that the unique solution is non-negative and satisfies the mass conservation property and an energy inequality.