N-Body Problem and Gas Dynamics in One Dimension
The aim of this article is to study the behavior of selfgravitating, one dimensional, systems from the point of view of Gas Dynamics.
The gas associated with Liouville’s equation behaves like a perfect gas of index 3. The entropy is linked with the central moment of order 3 of the frequency function.
The evolution of the water-bag model is described by a partial differential equation which generalizes that of Riemann for the propagation of waves.
The stability of the stationary solution for the water-bag model is investigated with the help of the Virial Theorem.