Local well-posedness of a system coupling compressible atmospheric dynamics and a micro-physics model of moisture in air

TL;DR

This paper proves the local-in-time well-posedness of a coupled system of compressible atmospheric dynamics and a refined moisture micro-physics model, including phase changes of water, for large initial data.

Contribution

It establishes the well-posedness of a complex coupled system combining compressible Navier-Stokes equations with an advanced moisture model.

Findings

Proved local-in-time existence and uniqueness of strong solutions.

Validated the well-posedness of the coupled atmospheric and moisture system.

Incorporated phase changes of water into the moisture model.

Abstract

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. 32:137--164, 2018). This micro-physics moisture model is a refinement of the one communicated by Klein and Majda (Theor. Comput. Fluid Dyn. 20:525--551, 2006), which serves as a foundation of multi-scale 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 micro-physics of moisture model incorporates the phase changes of water in moist air.