Global existence of weak solutions for the 3D incompressible Keller–Segel–Navier–Stokes equations with partial diffusion

Abstract

In this paper, we consider the Cauchy problem of the 3D incompressible Keller–Segel–Navier–Stokes equations with partial diffusion, namely we remove the diffusion Δ ρ . Using the damping effect of the growth term − ρ 3 and the geometry of axisymmetric flow without swirl, we prove the global existence of weak solutions for the system.