Higher Order Energy Conservation and Global Well-Posedness of Solutions for Gross-Pitaevskii Hierarchies

DOI10.1080/03605302.2013.816858zbMath1301.35146arXiv0906.2984OpenAlexW2964013734MaRDI QIDQ2926036

Nataša Pavlović, Thomas Chen

Publication date: 29 October 2014

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.2984

zbMATH Keywords

global well-posednessGross-Pitaevskii hierarchieshigher order energy functionals

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55) Many-body theory; quantum Hall effect (81V70)

Related Items (15)

The Gross-Pitaevskii hierarchy on general rectangular tori ⋮ Quantitative derivation and scattering of the 3D cubic NLS in the energy space ⋮ The unconditional uniqueness for the energy-supercritical NLS ⋮ Unconditional Uniqueness for the Cubic Gross-Pitaevskii Hierarchy via Quantum de Finetti ⋮ On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti ⋮ A rigorous derivation of the defocusing cubic nonlinear Schrödinger equation on \(\mathbb{T}^3\) from the dynamics of many-body quantum systems ⋮ Derivation of the cubic NLS and Gross-Pitaevskii hierarchy from manybody dynamics in \(d=3\) based on spacetime norms ⋮ Negative energy blowup results for the focusing Hartree hierarchy via identities of virial and localized virial type ⋮ The rigorous derivation of the \(\mathbb{T}^2\) focusing cubic NLS from 3D ⋮ An infinite sequence of conserved quantities for the cubic Gross–Pitaevskii hierarchy on ℝ ⋮ Randomization and the Gross-Pitaevskii hierarchy ⋮ Global well-posedness of the NLS system for infinitely many fermions ⋮ Local existence of solutions to randomized Gross-Pitaevskii hierarchies ⋮ The derivation of the \(\mathbb{T}^{3}\) energy-critical NLS from quantum many-body dynamics ⋮ Unconditional uniqueness for the energy-critical nonlinear Schrödinger equation on

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