Global bounded solution in an attraction repulsion Chemotaxis-Navier-Stokes system with Neumann and Dirichlet boundary conditions

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 ${\Vert n_0\Vert }_{L^1\left(\Omega \right)}$ in the explicit expressions for ${\Vert c_0\Vert }_{L^{\infty }\left(\Omega \right)}$ and attraction–repulsion coefficients.