About the Stability of Gas Balls
Gerhard Strohmer

  
  The presentation is concerned with the question of stability for the 
  spherically symmetric equilibrium of a barotropic fluid under the 
  influence of self gravitation with a
  free boundary without surface tension. This analysis proceeds by a study 
  of the linearization of the equation. Its solutions do not decay 
  exponentially,
  which makes it hard to derive nonlinear stability from linear stability. 
  We discuss some of the difficulties and the tools used for overcoming them.