Patterns Formation in a Self-Gravitating Isentropic Gas
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In this paper we consider a hydrodynamic model for the matter density distribution 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.
KeywordsInterstellar cloud Pattern formation Isentropic gas
The author is indebted to Prof. A. Prentice whose input and comments improved the quality of this paper.