Global Well-posedness of the 2D Stochastic Self-consistent Keller-Segel-Navier-Stokes System with Subcritical Cellular Mass

TL;DR

This paper proves the global well-posedness of a 2D stochastic Keller-Segel-Navier-Stokes system modeling cell motion in a fluid, establishing existence and uniqueness of solutions for subcritical cellular mass.

Contribution

It establishes the first global well-posedness result for the stochastic Keller-Segel-Navier-Stokes system with subcritical mass in two dimensions.

Findings

Existence of a unique mild solution globally in time.

Solution exists for subcritical cellular mass.

The system models cell-fluid interactions under stochastic influences.

Abstract

We consider a stochastic Keller-Segel-Navier-Stokes system in $R^2$ describing the collective motion of cells in an ambient stochastic fluid flow, where the cells are attracted by a chemical substance and transported by the ambient fluid velocity, and the fluid motion is self-consistently driven by forces induced by the cells. We prove the existence of a unique mild solution globally-in-time to the two-dimensional stochastic Keller-Segel-Navier-Stokes system with subcritical mass.