Communications in Mathematical Sciences

Volume 18 (2020)

Number 3

Qualitative analysis of an integrated chemotaxis-fluid model: global existence and extensibility criterion

Pages: 809 – 836



Jishan Fan (Department of Applied Mathematics, Nanjing Forestry University, Nanjing, China)

Lulu Jing (Center for Information, Nanjing Forestry University, Nanjing, China)

Gen Nakamura (Department of Mathematics, Hokkaido University, Sapporo, Japan)

Kun Zhao (Department of Mathematics, Tulane University, New Orleans, Louisiana, U.S.A.)


In this paper, we study the global existence and extensibility criterion of large-amplitude solutions to a chemotaxis-fluid model in bounded domains. The model under consideration is an integrated version of several recently studied models in bio-fluids, which is a coupled system of partial differential equations with strong nonlinearities. The results obtained in this paper appear to be among the first ones for the integrated model.


chemotaxis, Navier–Stokes equations, global existence, extensibility criterion

2010 Mathematics Subject Classification

35B40, 35D30, 35Q30

J. Fan was partially supported by the National Science Foundation of China No. 11971234. Support of K. Zhao comes partially from the Simons Foundation Collaboration Grant for Mathematicians No. 413028.

Received 14 September 2019

Accepted 30 November 2019

Published 30 June 2020