On a mathematical model of the rotating atmosphere of the Earth

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.