Chemical diffusion limit of a chemotaxis–Navier–Stokes system

Abstract

We consider the vanishing diffusion limit issue for the chemotaxis–Navier–Stokes system in ${\mathbb{R}}^3$. We show that as the chemical diffusion rate ε goes to zero, the solutions with $\epsilon >0$, converge to the non-diffusive solutions in the same Sobolev spaces of existence. The convergence rate is of order $O({\epsilon }^{1/2})$.

Keywords:

• Chemotaxis–Navier–Stokes
• vanishing diffusion limit
• convergence rate

2000 Mathematics Subject Classifications:

• 35A01
• 35K57
• 35Q92

Disclosure statement

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

Additional information

Funding

This work is supported by National Natural Science Foundation of China [grant number 11901139], China Postdoctoral Science Foundation [grant number 2019M651269], [grant number 2020T130151].