Decay of the solution to a reduced gravity two and a half layer equations

In this paper, we study a reduced gravity two and a half layer model in three-dimensional whole space R3R3. Under assumption of small initial data, we establish the unique global solution by energy method, furthermore, we obtain the time decay rates of the higher-order spatial derivatives of the solution by the method of spectral analysis and energy estimates if the initial data belongs to L1(R3)L1(R3) additionally.