Abstract: The Gross-Pitaevskii and Hartree hierarchies are infinite systems of coupled PDEs derived from the mean field theory of Bose gases. Due to their physical and mathematical relevance, the issues of well-posedness and uniqueness for these equations have recently been studied thoroughly using specific nonlinear and combinatorial techniques. In this talk, I will introduce a new approach based on a duality between these hierarchies and some Liouville's equations. And I will explain how such point of view yields several new results.
Joint work with Quentin Liard and Clément Rouffort.