Quantitative Derivation and Scattering of the 3D Cubic NLS in the Energy Space

被引：4
作者：
Chen, Xuwen [1 ]
Holmer, Justin [2 ]
机构：
[1] Univ Rochester, Dept Math, Rochester, NY 14627 USA
[2] Brown Univ, Dept Math, 151 Thayer St, Providence, RI 02912 USA
来源：
ANNALS OF PDE | 2022年 / 8卷 / 02期
关键词：
N-body quantum BBGKY hierarchy; Convergence rate; Klainerman-Machedon theory; Nonlinear scattering; Koch-Tataru U-V spaces; NONLINEAR SCHRODINGER-EQUATION; GROSS-PITAEVSKII HIERARCHY; GLOBAL WELL-POSEDNESS; BOSE-EINSTEIN CONDENSATION; MEAN-FIELD APPROXIMATION; MANY-BODY DYNAMICS; RIGOROUS DERIVATION; UNCONDITIONAL UNIQUENESS; INTERACTING BOSONS; PAIR EXCITATIONS;
D O I：
10.1007/s40818-022-00126-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the derivation of the defocusing cubic nonlinear Schrodinger equation (NLS) on R-3 from quantum N-body dynamics. We reformat the hierarchy approach with Klainerman-Machedon theory and prove a bi-scattering theorem for the NLS to obtain convergence rate estimates under H-1 regularity. The H(1 )convergence rate estimate we obtain is almost optimal for H(1 )datum, and immediately improves if we have any extra regularity on the limiting initial one-particle state.
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页数：39
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