A note on the global existence of a two-dimensional chemotaxis-Navier–Stokes system

ABSTRACT

In this short note, we establish the global existence of weak solutions and classical solutions to the two-dimensional chemotaxis-Navier–Stokes system for both the Cauchy problem and the initial-boundary value problem under some suitable small conditions on the initial data. In particular, we improve the recent results obtained by Duan–Li–Xiang (J. Differential Equations, 2017).

KEYWORDS:

• Chemotaxis
• Navier–Stokes
• global existence

AMS SUBJECT CLASSIFICATIONS:

• 35K55
• 35Q92
• 35Q35
• 92C17

Acknowledgements

The authors are very grateful to the referees for their detailed comments and valuable suggestions, which greatly improved the manuscript.

Notes

No potential conflict of interest was reported by the authors.