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In this note, we provide two results concerning the global well-posedness anddecay of solutions to an asymptotic model describing the nonlinear wavepropagation in the troposphere, namely, the morning glory phenomenon. The proofof the first result combines a pointwise estimate together with someinterpolation inequalities to close the energy estimates in Sobolev spaces. Thesecond proof relies on suitable Wiener-like functional spaces.

Well-posedness and decay for a nonlinear propagation wave model in atmospheric flows