Earth, Moon, and Planets

, Volume 121, Issue 1–2, pp 1–12 | Cite as

Patterns Formation in a Self-Gravitating Isentropic Gas

  • Mayer Humi


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.


Interstellar cloud Pattern formation Isentropic gas 



The author is indebted to Prof. A. Prentice whose input and comments improved the quality of this paper.


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© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Mathematical SciencesWorcester Polytechnic InstituteWorcesterUSA

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