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 R3. 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 Ḣ−s(0⩽s<32).
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