Global existence and large time behavior for a two-dimensional chemotaxis–shallow water system

Abstract This paper concerns the chemotaxis–shallow water system in two dimensional whole spaces. We first establish the global existence of strong solution under the condition that the initial data are close to the constant equilibrium state in H N ( R 2 ) ( N ≥ 3 ) -framework. Then, the optimal time decay rates of the global solution are obtained by the method of energy estimates, if the initial data belong to H ˙ − s ( R 2 ) ( 0 s 1 ) additionally.