  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.
