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.