Global solvability to a two competing species chemotaxis Navier-Stokes system with singular sensitivity

In this paper, we deal with a two-species chemotaxis Navier-Stokes system with singular sensitivity under the homogeneous Neumann boundary conditions in a bounded domain Ω ⊂ R 2 with smooth boundary.For any appropriately regular initial data, we prove that the system has a global classical solution when χ := max{χ 1 , χ 2 } < 1.Moreover, we showed the global boundedness of the solution for sufficiently large b 1 and b 2 .