Global existence and boundedness in a two-species chemotaxis-fluid system with indirect pursuit-evasion interaction

Abstract This paper investigates a two-species chemotaxis-fluid system with indirect pursuit-evasion interaction in a bounded domain with smooth boundary. Under suitably regular initial data and no-flux/no-flux/no-flux/no-flux/Dirichlet boundary conditions, we prove that the system possesses a global bounded classical solution in the two-dimensional and three-dimensional cases. Our results extend the result obtained in previously known ones and partly result is new.