A Bose gas at zero temperature is described by a mean-field that satisfies the cubic nonlinear Schr¨odinger equation (NLS) otherwise known as the Gross- Pitaevski equation. The mean field describes the evolution of the condensate in an average sense. I will describe a technique that introduces pair correlations in the evolution of condensate. The resulting approximation tracks the evolution of the condensate in norm provided that the pair wave-function satisfies an interesting system of coupled NLS equations. I will discuss the nonlinear structure of the NLS system as well as a novel approach to the question of the global existence of solutions of the system.
Manoussos Grillakis is a Professor of Mathematics at the University of Maryland in College Park. His research interests are in Analysis and Partial Differential Equations. In particular, he is interested in the Analysis of equations that arise in Physical problems and describes the evolution of waves.