Uniqueness of solutions to the 3D quintic Gross-Pitaevskii hierarchy

作者：Hong Younghun^*; Tahaferro Kenneth; Xie Zhihui

来源：Journal of Functional Analysis, 2016, 270(1): 34-67.

DOI：10.1016/j.jfa.2015.10.003

• Gross-Pitaevskii hierarchy
• Nonlinear Schrodinger equation
• Uniqueness
• Quantum de Finetti theorem

In this paper, we study solutions to the three-dimensional quintic Gross-Pitaevsldi hierarchy. We prove unconditional uniqueness among all small solutions in the critical space h(1) (which corresponds to H-1 on the NLS level). With slight modifications to the proof, we also prove unconditional uniqueness of solutions to the Hartree hierarchy without a smallness condition. Our proof uses the quantum de Finetti theorem, and is an extension of the work by Chen, Hainzl, Pavlovic, and Seiringer [9], and our previous work [32].

• 出版日期2016-1-1