Boundedness in a three-dimensional Keller–Segel–Stokes system with subcritical sensitivity

Abstract

We consider a quasilinear Keller–Segel system with density-dependent migration rates, coupled to the incompressible Stokes equations through transport and buoyancy. By means of an apparently novel approach based on certain conditional estimates for the taxis gradient and the fluid field, for diffusion rates asymptotically controllable by power-tape majorants and minorants a result on global existence and boundedness is derived under an essentially optimal condition on the strength of cross-diffusion relative to diffusion.