Global existence and asymptotic stability of the fractional chemotaxis–fluid system in R3

Abstract In this paper, we consider a model arising from biology, consisting of fractional chemotaxis equations coupled to viscous incompressible fluid equations throughout transport and external force in R 3 . We establish the existence and uniqueness of global solution with small initial data by combining the local existence and a priori estimates as well as continuation argument. Moreover, the decay rates of the solutions and their higher-order spatial derivatives are established towards the equilibrium by introducing the negative Sobolev space H − s ( 0 ⩽ s 3 2 ).