Journal of Mathematical Physics
In this paper we develop a simple model for the steady state of two-dimensional self-gravitating incompressible gas which is based on the hydrodynamic equations for stratified fluid. These equations are then reduced to a system of two equations for the mass density and the gravitational field. Analytical analysis and numerical solutions of these equations under different modeling assumptions (with special attention to the isothermal case) are then used to study the structure of the resulting steady state of the fluid.
Copyright 2006 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Mathematical Physics 47(9) and may be found at http://link.aip.org/link/doi/10.1063/1.2344852.
Humi, M. (2006). Steady States of Self-Gravitating Incompressible Fluid in Two Dimensions. Journal of Mathematical Physics, 47(9) http://dx.doi.org/10.1063/1.2344852