Global existence of free-energy solutions to the 2D Patlak--Keller--Segel--Navier--Stokes system with critical and subcritical mass

TL;DR

This paper proves the global existence of free-energy solutions for a coupled 2D system modeling cell movement and fluid flow, extending understanding to critical and subcritical mass regimes.

Contribution

It establishes the first rigorous proof of global solutions for the 2D Patlak-Keller-Segel-Navier-Stokes system with critical and subcritical mass.

Findings

Global existence of solutions proven for critical and subcritical mass.

Extension of previous results to coupled cell-fluid systems.

Provides mathematical framework for analyzing chemotaxis-fluid interactions.

Abstract

We consider a coupled Patlak-Keller-Segel-Navier-Stokes system in $\mathbb{R}^2$ that describes the collective motion of cells and fluid flow, where the cells are attracted by a chemical substance and transported by ambient fluid velocity, and the fluid flow is forced by the friction induced by the cells. The main result of the paper is to show the global existence of free-energy solutions to the 2D Patlak-Keller-Segel-Navier-Stokes system with critical and subcritical mass.