Global classical solution and stability to a coupled chemotaxis-fluid model with logistic source

Abstract

In this paper, we deal with a coupled chemotaxis-fluid model with logistic source γn− µn2. We prove the existence of global classical solution for the chemotaxis-Stokes system in a bounded domain Ω ⊂ R3 for any large initial data. On the basis of this, we further prove that if γ > 0, the zero solution is not stable; if γ = 0, the zero solution is globally asymptotically stable; and if 0 < γ < 16µ2, the nontrivial steady state µγµγ , 0 is globally asymptotically stable.