The Euler-Poisson system in plasma physics

Dong Li
Mathematics, University of Iowa

(November 1, 2011 10:30 AM - 11:30 AM)

The Euler-Poisson system in plasma physics

Abstract

The Euler-Poisson system is a fundamental two-fluid model in physics. It describes the motion of ions and electrons coupled through their self-consistent electric field. For the three-dimensional case Guo '98 first constructed a smooth global solution around the constant-density equilibrium by using a Klein-Gordon dispersive effect. It has been long conjectured that same results should also hold in the two-dimensional case. The main issues in 2D are slow dispersion, quasilinearity and certain nonlocal obstructions in the nonlinearity. I will discuss some recent advances which lead to the complete resolution of this conjecture.