Institute of Mathematics for Industry

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Existence and uniqueness of solutions for the Hartree and Gross-Pitaevskii hierarchy equations


Hold Date 2019-07-05 16:30~2019-07-05 18:00

Place IMI Conference Room(W1-D-414), West Zone 1, Ito campus, Kyushu University

Object person  

Speaker Zied Ammari (Universite Rennes 1)

Abstract:
The Gross-Pitaevskii and Hartree hierarchies are infinite systems of coupled PDEs derived from the mean field theory of quantum 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 certain transport equations of probability measures.  And I will explain how such point of view yields new well-posedness and uniqueness results.