  In this paper, we investigate the two-dimensional
Patlak-Keller-Segel-Navier-Stokes system perturbed around the Poiseuille flow
$(Ay^2,0)^{\top}$ and show that the solutions to this system are global in time
if the Poiseuille flow is sufficiently strong in the sense of amplitude A large
enough. This seems to be the first result showing that the Poiseuille flow can
suppress the chemotactic blow-up of the solution to chemotaxis-fluid system.
Our proof will be based on a weighted energy method together with the linear
enhanced dissipation established by Coti Zelati-Elgindi-Widmayer (Comm. Math.
Phys. 378 (2020) 987-1010).
