Local energy estimates and global solvability in a three-dimensional chemotaxis-fluid system with prescribed signal on the boundary

The chemotaxis-Stokes system{nt+u·∇n=Δn−∇·(n∇c),ct+u·∇c=Δc−nc,ut=Δu+∇P+n∇ϕ, ∇·u=0, (⋆)is considered in a bounded domain Ω⊂R3 with smooth boundary. The corresponding solution theory is quite wel...