Unconditional Uniqueness of the cubic Gross-Pitaevskii Hierarchy with Low Regularity

Abstract

In this paper, we establish the unconditional uniqueness of solutions to the cubic Gross-Pitaevskii hierarchy on ${\mathbb{R}}^d$ in a low regularity Sobolev type space. More precisely, we reduce the regularity $s$ down to the currently known regularity requirement for unconditional uniqueness of solutions to the cubic nonlinear Schrödinger equation ($s\ge \frac{d}{6}$ if $d=1,2$ and $s>s_c=\frac{d-2}{2}$ if $d\ge 3$). In such a way, we extend the recent work of Chen-Hainzl-Pavlović-Seiringer.

26 pages, 1 figure

References in corpus (2)

• On the uniqueness of solutions to the Gross-Pitaevskii hierarchy
• On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti

Cited by in corpus (3)

• Correlation structures, Many-body Scattering Processes and the Derivation of the Gross-Pitaevskii Hierarchy
• On the unconditional uniqueness of solutions to the infinite radial Chern-Simons-Schrödinger hierarchy
• Uniqueness of solutions to the 3D quintic Gross-Pitaevskii Hierarchy