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June  2019, 39(6): 3413-3441. doi: 10.3934/dcds.2019141

## Global existence of almost energy solution to the two-dimensional chemotaxis-Navier-Stokes equations with partial diffusion

 The School of Mathematics and System Science, Beihang University, Beijing 100191, China

* Corresponding author: Xiaoxin Zheng

Received  August 2018 Revised  December 2018 Published  February 2019

In this paper, we study Cauchy problem of the two-dimensional chemotaxis-Navier-Stokes equations with partial diffusion. Taking advantage of a coupling structure of the equations and using the damping effect of the growth term $g(n)$, we obtain the necessary estimates of solution $(n,c,u)$ without the diffusion term $\Delta n$. These uniform estimates enable us to establish the global-in-time existence of almost weak solutions for the system.

Citation: Laiqing Meng, Jia Yuan, Xiaoxin Zheng. Global existence of almost energy solution to the two-dimensional chemotaxis-Navier-Stokes equations with partial diffusion. Discrete & Continuous Dynamical Systems - A, 2019, 39 (6) : 3413-3441. doi: 10.3934/dcds.2019141
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