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 $\mathrm{\Delta }\rho$. Using the damping effect of the growth term $-{\rho }^3$ and the geometry of axisymmetric flow without swirl, we prove the global existence of weak solutions for the system.

Keywords:

• Keller–Segel equations
• Navier–Stokes equations
• global existence
• weak solutions

AMS Subject Classifications:

• 35K55
• 35Q92
• 35Q35
• 92C17

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Xiaoyu Chen was partially supported by the Postgraduate Innovation Foundation of Hebei University [grant number HBU2022ss013]. Q. Zhang was partially supported by the Natural Science Foundation of Hebei Province [grant number A2020201014]; the Second Batch of Young Talents of Hebei Province; Nonlinear Analysis Innovation Team of Hebei University.