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

This study investigates a climate dynamics model that incorporates topographical effects and the phase transformation of water vapor. The system comprises the Navier-Stokes equations, the temperature equation, the specific humidity equation, and the water content equation, all adhering to principles of energy conservation. Applying energy estimation methods, the Helmholtz-Weyl decomposition theorem, and the Brezis-Wainger inequality, we derive high-order a priori estimates for state functions. Subsequently, based on the initial data assumptions V-0 is an element of H-4(Omega), T-0 ',q(0),m(omega 0)is an element of H-2(Omega), we can prove that a strong solution to this system exists globally in time and establish the uniqueness of the global strong solution.