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

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.