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

  • * Corresponding author: Xiaoxin Zheng

    * Corresponding author: Xiaoxin Zheng
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  • 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.

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


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