Ohio State University
I will consider the Vlasov-Poisson Equations for a collisionless plasma of electrons moving through positively charged ions with measure-valued (electron sheet) initial data. (An electron sheet describes a concentrated beam of particles.) I will approximate this problem by a sequence of smooth problems in several different ways including mollifying the initial data, the mollified kernel computational particle method, and the "viscous" regularizations by
the pseudo-Fokker-Planck and Fokker-Planck equations. I will use a combination of theoretical, analytical and numerical results to examine the limit of vanishing regularization for each of these methods. The surprising conclusion is that these limits are not necessarily equal.
Finally, I will present connections between the current work and the problem which motivated it, namely, trying to understand the limit of vanishing regularization for different regularizations of the incompressible Euler Equations with vortex sheet initial data.
Please join us for refreshments before the lecture at 2:30p.m. in room 353 Jabara Hall.
[ Fall 2000]