Abstract
In this paper, we consider the large time behavior of solution for the chemotaxis-shallow water system in two-dimension by the method of frequency decomposition. First, we construct the Green's function of the linearized system and get the corresponding estimates for low frequency part. Then, we introduce an energy method we named ‘double cycle method’ to get the decay rate for high frequency part. Due to the dissipative mechanism of this system, the high frequency part decays faster than the low frequency part.
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