Local Well-Posedness of a System Coupling Compressible Atmospheric Dynamics and a Microphysics Model of Moisture in Air

We establish here the local-in-time well-posedness of strong solutions with large initial data to a system coupling compressible atmospheric dynamics with a refined moisture model introduced in Hittmeir and Klein (Theor. Comput. Fluid Dyn., 32 (2018), pp. 137-164). This microphysics moisture model is a refinement of the one communicated by Klein and Majda (Theor. Comput. Fluid Dyn., 20 (2006), pp. 525-551), which serves as a foundation of multiscale asymptotic expansions for moist deep convection in the atmosphere. Specifically, we show, in this paper, that the system of compressible Navier-Stokes equations coupled with the moisture dynamics is well-posed. In particular, the microphysics of moisture model incorporates the phase changes of water in moist air.