Equation system describing the radiation intensity and the air motion with the water phase transition

TL;DR

This paper develops a mathematical model coupling air motion, radiation intensity, water droplets, and phase transition, proving local existence and uniqueness of solutions, improving previous models by eliminating regularization approximations.

Contribution

It introduces an improved equation system that accurately models water phase transition and radiation effects in air motion, with rigorous proof of solution existence and uniqueness.

Findings

Proved local existence and uniqueness of solutions.

Enhanced previous models by removing regularization approximations.

Established conditions for the well-posedness of the coupled system.

Abstract

In this paper we consider the equation system describing the motion of the air and the variation of the radiation intensity and the quantity of water droplets in the air, including also the process of water phase transition. Under a suitable condition we prove the existence and uniqueness of the local solution. By eliminating the approximation by regularization of vapor density and by including the equation of radiation, this result improves previous ones.