Boundedness in chemotaxis-Stokes system with rotational flux term

We consider the following chemotaxis-Stokessystem with rotation nt=Δn−∇⋅(nS(x,n,c)⋅∇c)−u⋅∇n,ct=Δc−f(x,n,c)−u⋅∇c,ut=Δu+∇P+n∇ϕ,∇⋅u=0in Ω×(0,T), subject to the non-flux boundary conditions for n andc, as well as the Dirichlet boundary condition for u, where the bounded smooth domain Ω⊂R3, the matrix-valued function S∈C2(Ω̄×[0,∞)2;R3×3) fulfills |S(x,n,c)|≤S0(c)(1+n)θ for all (x,n,c)∈Ω̄×[0,∞)2 with S0 nondecreasing, and f∈C1(Ω̄×[0,∞)2;R) satisfies 0≤f(x,n,c)≤f0(c)(n+1) with f0 nondecreasing and f(x,n,0)=0. It was proved that for any θ>0, the initial-boundary value problem possesses a unique globally bounded classical solution.