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Unique Solvability of a System of Ordinary Differential Equations Modeling a Warm Cloud Parcel

https://doi.org/10.1137/19M1267751

Abstract

We analyze the solvability of a system of ordinary differential equations modeling a warm cloud. A unique feature of this model is the automatic onset of nucleation when the moist air parcel becomes supersaturated; this is made possible by a non-Lipschitz right-hand side of the differential equation, which allows for nontrivial smooth solutions. Here we prove under mild assumptions on the external forcing that this system of equations has a unique physically consistent solution, i.e., a solution with a nonzero droplet population in the supersaturated regime.

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