In this paper we consider a hydrodynamic model for the matter density distri-bution in a self gravitating, isentropic 2-d disk of gas where the isentropy coefficient is allowed to be a function of position. For this model we prove analytically the existence of steady state and time dependent solutions in which the matter density in the disk is oscillatory and pattern forming. This research is motivated in part by recent astronomical
observations and Laplace conjecture (made in 1796) that planetary systems evolve from a family of isolated rings that are formed within a primitive interstellar gas cloud.

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