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

Laiqing Meng; Jia Yuan; Xiaoxin Zheng

doi:10.3934/dcds.2019141

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2019, Volume 39, Issue 6: 3413-3441. Doi: 10.3934/dcds.2019141

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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
^* Corresponding author: Xiaoxin Zheng

Received: July 31, 2018

Revised: November 30, 2018

Published: February 2019

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Abstract

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.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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