EXISTENCE AND NONLINEAR STABILITY O F DYNAMIC SOLUTIONS T O THE VLASOV EQUATION UNDER A 5 POTENTIAL

permission of the author. Supervisor: Dr. R. Illner. This dissertation analyzes the existence and nonlinear stability of spherically symmetric dynamic solutions to the Vlasov equation under an inverse-square potential, known as the Vlasov-Manev system. This is an interesting mathematical problem because compared to a potential of the form-&, where 1 < a < 2, the singularities which are encountered are much stronger and the analytical problems encountered are much more difficult. The first two Chapters give a brief historical background and necessary introductory material, as well as a summary of what is to follow. In the subsequent Chapters, several formulae for the potential and the force term which would apply in a spherically symmetric dynamic solution under an inverse-square potential are derived. Some of these are particularly well suited to solutions which have compact support. With these formulae in hand, some examples of anisotropic steady state solutions which are compactly supported are developed. The two ex