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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, ThomasPavlovic, Natasa Keywords: Mean Field LimitsQuantum Many BodyCauchy ProblemNonlinear SchrodingerGross-PitaevskiiBBGKY Hierarchy Issue Date: 8-Jan-2011 Series/Report no.: Analysis and Applied Mathematics Seminar2011-01-07 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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