Abstract
This paper deals with an attraction–repulsion Chemotaxis-Navier–Stokes system with Dirichlet boundary for the attraction signal and Neumann boundary for the repulsion signal. Based on the work of Winkler (2020) and Wang et al. (2022), by using a series estimates, it is shown that in two dimension the classical solution of the system is globally bounded, under the condition of small initial values ‖n0‖L1(Ω) in the explicit expressions for ‖c0‖L∞(Ω) and attraction–repulsion coefficients.
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