  In this paper, we proposed a coupled Patlak-Keller-Segel-Navier-Stokes
system, which has dissipative free energy. On the plane $\rr^2$, if the total
mass of the cells is strictly less than $8\pi$, classical solutions exist for
any finite time, and their $H^s$-Sobolev norms are almost uniformly bounded in
time. For the radially symmetric solutions, this $8\pi$-mass threshold is
critical. On the torus $\mathbb{T}^2$, the solutions are uniformly bounded in
time under the same mass constraint.
