Global existence of the strong solution to the climate dynamics model with topography effects and phase transformation of water vapor.

This article focuses on the global existence and uniqueness of strong solutions to a climate dynamics model that incorporates topographical effects and the phase transformation of water vapor. The model is formulated through a system of partial differential equations including the Navier–Stokes equations, temperature, specific humidity, and liquid water content equations, all consistent with energy conservation. Using advanced mathematical tools such as the Helmholtz–Weyl decomposition theorem and the Brezis–Wainger inequality, the authors establish high-order a priori estimates and prove that, under suitable initial data regularity assumptions, the strong solution exists globally in time and is unique. The study addresses challenges posed by nonlinear terms and boundary conditions by deriving detailed energy inequalities and employing a modified smooth velocity field to ensure well-posedness without common approximations like the anelastic approximation.