A COUPLED KELLER-SEGEL-STOKES MODEL: GLOBAL EXISTENCE FOR SMALL INITIAL DATA AND BLOW-UP DELAY

Abstract

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 8 pi, which is the critical mass for the system without fluid.