Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590922 | Journal of Functional Analysis | 2011 | 39 Pages |
Abstract
We investigate the dynamics of a boson gas with three-body interactions in dimensions d=1,2. We prove that in the limit of infinite particle number, the BBGKY hierarchy of k-particle marginals converges to a limiting (Gross–Pitaevskii (GP)) hierarchy for which we prove existence and uniqueness of solutions. Factorized solutions of the GP hierarchy are shown to be determined by solutions of a quintic nonlinear Schrödinger equation. Our proof is based on, and extends, methods of Erdös–Schlein–Yau, Klainerman–Machedon, and Kirkpatrick–Schlein–Staffilani.
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