On a mathematical model of the rotating atmosphere of the Earth

TL;DR

This paper analyzes a simplified mathematical model of Earth's rotating atmosphere using compressible Euler equations, providing fundamental results and rigorous inquiry into atmospheric motion modeling.

Contribution

It introduces a mathematically rigorous analysis of the Earth's rotating atmosphere using the compressible Euler equations with a barotropic ideal gas model.

Findings

Fundamental results on atmospheric motion modeling

Mathematically rigorous analysis of rotating atmosphere

Identification of open problems in the model

Abstract

In meteorology the analysis of motions of the atmosphere on the Earth has been done using various mathematical models and using various approximations. In this article as the simplest model the compressible Euler equations with barotropic equation of state of the ideal gas is analyzed under the co-ordinate system which rotates with constant angular velocity. Mathematically rigorous inquiry is tried. Although problems remain to be open, some fundamental results are exhibited.