Mathematical analysis of the continuum model of astronomical objects

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We considered the mathematical modelization of astronomical objects by the continuum approximation (based on the basic equation of compressible viscous fluid), and verified the justification of our modeling through mathematical analysis. We obtained the following main two results : (1) On the case that both the model is composed of ideal gas and the gaseous motion is spacially one-dimensional, we proved that the motion of the gas exists for a long time stably without taking the smallness on the size of the initial data. (2) On the case that the gaseous motion is spherically symmetric in spacially three-dimension, we proved the long time stability of the motion of the gas as with the case (1).