Global well-posedness of strong solutions to a model for the morning glory cloud

In this paper, we investigate the global well-posedness of strong solution to a model recently derived by Constantin-Johnson \cite{CaJo} which describes the nonlinear wave propagation in the troposphere, especially for the morning glory cloud. Assuming that the initial velocity $v_0\in H^1$ and the thermodynamic forcing term $K\in L^2(0,T;L^2)$, we show that there exists a unique global strong solution to the initial boundary value problem of this system. Similar result was only known before for sufficiently small initial data in the existing literature.