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. We study a system consisting of the elliptic-parabolic Keller–Segel equations coupled to Stokes equations by transport and gravitational forcing. We show global-in-time existence of solutions for small initial mass in 2D. In 3D we establish global existence assuming that the initial L 3/2-norm is small. Moreover, we give numerical evidence that for this extension of the Keller–Segel system in 2D, solutions exist with mass above 8π, which is the critical mass for the system without fluid.

A coupled Keller–Segel–Stokes model: global existence for small initial data and blow-up delay