Kinetic FRG Young Researchers Workshop
March 2-5, 2009

CSIC Building (#406), Seminar Room 4122.

Weak Solution and Critical Thresholds for the One-dimensional Vlasov-Poisson Equations

Dr. Dongming Wei

University of Wisconsin - Madison

Abstract:  We give an explicit weak solution of the one-component Vlasov-Poisson equations in a single space dimension with smooth electron sheet initial data. Moreover, we give sharp conditions on whether the moments of this weak solution will blow up or not. It depends on whether or not the initial configuration of the density and velocity crosses a critical threshold. After the critical time, we construct a weak solution of the Vlasov-Poisson equation based on an multi-valued solution to the Euler-Poisson equation.