  In this paper, we study the global well-posedness of a coupled system of
kinetic and fluid equations. More precisely, we establish the global existence
of weak solutions for Navier-Stokes-BGK system consisting of the BGK model of
Boltzmann equation and incompressible Navier-Stokes equations coupled through a
drag forcing term. This is achieved by combining weak compactness of the
particle interaction operator based on Dunford-Pettis theorem, strong
compactness of macroscopic fields of the kinetic part relied on velocity
averaging lemma and a high order moment estimate, and strong compactness of the
fluid part by Aubin-Lions lemma.
