The equations of the atmosphere with humidity and saturation: Uniqueness and physical bounds

•We study the equations of moist air with saturation and phase-change.•A mathematical formulation and existence of solutions were established in an earlier paper.•Uniqueness of solutions is proved to ensure the physical validity of our formulation.•Regularity properties and physical bounds on the solutions are also established.

In continuation of an earlier work (Coti Zelati and Temam, 2012)  [8] devoted to the mathematical formulation and existence of solutions for the system of moist atmosphere with saturation, we address, here, the question of the uniqueness of solutions, which is essential for giving a physical justification for the analysis of the model in Coti Zelati and Temam (2012)  [8]. We also derive some physical bounds on the solution as well as additional results of regularity of the solutions.