Asymptotic behaviors of solutions for an aerobatic model coupled to   fluid equations
  We consider coupled system of Keller-Segel type equations and the incompressible Navier-Stokes equations in spatial dimension two. We show temporal decay estimates of solutions with small initial data and obtain their asymptotic profiles as time tends to infinity. 
Myeongju Chae, Kyungkeun Kang and Jihoon Lee
math.AP