Mathematical Study of Some Models of the Atmosphere Dynamics Counting with Heat Transfer and Humidity

摘要

We investigate some mathematical properties of the solutions of various PDE systems which describe fluid dynamics of the Atmosphere with consideration of heat transfer, humidity and water content. For nonlinear PDE system of seven unknown functions, we prove the existence of the weak solution. For differential operators generated by the corresponding linear system, we find the essential spectrum of inner vibrations and localize the part of the complex plane for all the eigenvalues. We compare the obtained results with our previous study of the spectral properties of the compressible fluid. The results of this paper may be applied in the theoretical and computational study of the Atmosphere of the Earth.