On the Uniqueness of Solutions to the Gross-Pitaevskii Hierarchy
By S. Klainerman, M. Machedon. 2007
158 citations recorded by the source corpus.
The purpose of this note is to give a new proof of uniqueness of the Gross-Pitaevskii hierarchy, first established in [1], in a different space, based on space-time estimates similar in spirit to those of [2].
Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/95dd50a02060d53dc14b81bc6bd8649925666f54
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In Applied Mathematics
In Mathematical Physics
- Dionisios Margetis
- M. Grillakis
- Niels Benedikter
- M. Machedon
- Yongyong Cai
- Weizhu Bao
- B. Schlein
- M. Porta
In Statistical and Nonlinear Physics
- Niels Benedikter
- M. Porta
- Dionisios Margetis
- M. Grillakis
- M. Machedon
- Yongyong Cai
- Weizhu Bao
- B. Schlein
Citations in the corpus
- Effective Evolution Equations from Quantum Dynamics (2015, background): “10) was later proposed in [43] based on certain space-time estimates for the densities γ̃ (k) ∞,t.”
- Second-Order Corrections to Mean Field Evolution of Weakly Interacting Bosons. I. (2009, methodology): “The precise meaning of this approximation as well as its rigorous justification were studied within the PDE setting by Erdös, Schlein, Yau [6–10] via Bogoliubov-Born-Green-Kirkwood-Yvon hierarchies for reduced density matrices (see also Klainerman and Machedon, [18], for a simplification of the uni”
- Mathematical Models and Numerical Methods for Bose-Einstein Condensation (2012, background): “; and for dynamics, Yau et al. [42] established the validity of the GPE (2.8) as an approximation for (2.3), which inspired great interests in the study on dynamics for such many body system recently [35, 36, 54]. The above GPE (2.8) is a very simple equation, which is very convenient for mathematic”