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Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/25753

Title: Mean Field Limits for Interacting Bose Gases and the Cauchy Problem for Gross-Pitaevskii Hierarchies
Authors: Chen, Thomas
Pavlovic, Natasa
Keywords: Mean Field Limits
Quantum Many Body
Cauchy Problem
Nonlinear Schrodinger
Gross-Pitaevskii
BBGKY Hierarchy
Issue Date: 8-Jan-2011
Series/Report no.: Analysis and Applied Mathematics Seminar
2011-01-07
Abstract: This talk surveys some recent results, all based on joint work with Natasa Pavlovic, related to the dynamics of Bose gases, and the Cauchy problem for Gross-Pitaevskii (GP) hierarchies. A GP hierarchy is an infinite system of coupled partial differential equations describing an interacting Bose gas in a mean field limit. First, we describe how the quintic nonlinear Schrodinger equation is derived from an N-body Schrodinger system with 3-body interactions and an associated GP hierarchy.Then, the local well-posedness theory for more general GP hierarchies is addressed, for focusing, defocusing, cubic and quintic interactions. In particular, the occurrence of blowup solutions is discussed (joint work with N. Pavlovic and N. Tzirakis). Furthermore, we present new conserved energy functionals which we apply to extend local to global well-posedness.
Description: Thomas Chen was invited to speak in the Analysis and Applied Math Seminar by I.M. Sigal.
URI: http://hdl.handle.net/1807/25753
Appears in Collections:Department of Mathematics

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