On the uniqueness of solutions to the Gross-Pitaevskii hierarchy

Abstract

We give a new proof of uniqueness of solutions to the Gross-Pitaevskii hierarchy, first established by Erdos, Schlein and Yau, in a different space, based on space-time estimates.

References in corpus (1)

• Derivation of the Cubic Non-linear Schrödinger Equation from Quantum Dynamics of Many-Body Systems

Cited by in corpus (70)

• Mathematical theory and numerical methods for Bose-Einstein condensation
• On the Dynamics of Large Particle Systems in the Mean Field Limit
• Second-order corrections to mean field evolution for weakly interacting Bosons. I
• Rigorous Derivation of the Gross-Pitaevskii Equation with a Large Interaction Potential
• Pair excitations and the mean field approximation of interacting Bosons, I
• Second-order corrections to mean-field evolution of weakly interacting Bosons, II
• Unconditional uniqueness for the cubic Gross-Pitaevskii hierarchy via quantum de Finetti
• Gross-Pitaevskii Dynamics for Bose-Einstein Condensates
• Focusing Quantum Many-body Dynamics: The Rigorous Derivation of the 1D Focusing Cubic Nonlinear Schrödinger Equation
• Second order corrections to mean field evolution for weakly interacting Bosons in the case of 3-body interactions
• On the Klainerman-Machedon Conjecture of the Quantum BBGKY Hierarchy with Self-interaction
• On the Rigorous Derivation of the 3D Cubic Nonlinear Schrödinger Equation with A Quadratic Trap
• Derivation of the cubic NLS and Gross-Pitaevskii hierarchy from manybody dynamics in $d=3$ based on spacetime norms
• Pair excitations and the mean field approximation of interacting Bosons, II
• On the uniqueness of solutions to the periodic 3D Gross-Pitaevskii hierarchy
• Energy conservation and blowup of solutions for focusing Gross-Pitaevskii hierarchies
• On the rate of convergence for the mean field approximation of many-body quantum dynamics
• On the rigorous derivation of the 2D cubic nonlinear Schrödinger equation from 3D quantum many-body dynamics
• Derivation of Effective Evolution Equations from Microscopic Quantum Dynamics
• A rigorous derivation of the defocusing cubic nonlinear Schrödinger equation on ${\mathbb{T}}^3$ from the dynamics of many-body quantum systems
• Global Well-posedness of the NLS System for infinitely many fermions
• Correlation structures, Many-body Scattering Processes and the Derivation of the Gross-Pitaevskii Hierarchy
• The Rigorous Derivation of the 2D Cubic Focusing NLS from Quantum Many-body Evolution
• Collapsing Estimates and the Rigorous Derivation of the 2d Cubic Nonlinear Schrödinger Equation with Anisotropic Switchable Quadratic Traps
• Beyond mean field: On the role of pair excitations in the evolution of condensates
• The Derivation of the ${\mathbb{T}}^3$ Energy-critical NLS from Quantum Many-body Dynamics
• On the unconditional uniqueness of solutions to the infinite radial Chern-Simons-Schrödinger hierarchy
• Higher order corrections to the mean-field description of the dynamics of interacting bosons
• Randomization and the Gross-Pitaevskii hierarchy
• On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti
• The Gross-Pitaevskii hierarchy on general rectangular tori
• The Hartree-von Neumann limit of many body dynamics
• Unconditional Uniqueness Results for the Nonlinear Schrödinger Equation
• Local existence of solutions to Randomized Gross-Pitaevskii hierarchies
• The rigorous derivation of the ${\mathbb{T}}^2$ focusing cubic NLS from 3D
• Quantitative Derivation and Scattering of the 3D Cubic NLS in the Energy Space
• The unconditional uniqueness for the energy-supercritical NLS
• Uniqueness of Solutions to the Spectral Hierarchy in Kinetic Wave Turbulence Theory
• Derivation of the time dependent Gross-Pitaevskii equation for a class of non purely positive potentials
• On the Cauchy problem for focusing and defocusing Gross-Pitaevskii hierarchies
• Unconditional Uniqueness of the cubic Gross-Pitaevskii Hierarchy with Low Regularity
• Convergence rate towards the fractional Hartree-equation with singular potentials in higher Sobolev norms
• The Unconditional Uniqueness for the Energy-critical Nonlinear Schrödinger Equation on ${\mathbb{T}}^4$
• On the Cauchy problem for Gross-Pitaevskii hierarchies
• Higher order energy conservation and global wellposedness of solutions for Gross-Pitaevskii hierarchies
• Mean field propagation of Wigner measures and BBGKY hierarchies for general bosonic states
• Convolution estimates and the Gross-Pitaevskii hierarchy
• Apriori Estimates for Many-Body Hamiltonian Evolution of Interacting Boson System
• Derivation of a Nonlinear Schrödinger Equation with a General power-type nonlinerity
• A Central Limit Theorem in Many-Body Quantum Dynamics
• Derivation of the two dimensional nonlinear Schrodinger equation from many body quantum dynamics
• The quintic NLS as the mean field limit of a Boson gas with three-body interactions
• Uniqueness of solutions to the 3D quintic Gross-Pitaevskii Hierarchy
• Well/Ill-posedness of the Boltzmann Equation with Soft Potential
• Well/ill-posedness bifurcation for the Boltzmann equation with constant collision kernel
• An infinite sequence of conserved quantities for the cubic Gross-Pitaevskii hierarchy on $\mathbb{R}$
• On the mean-field and semiclassical limit from quantum $N$-body dynamics
• The Hartree equation with a constant magnetic field: Well-posedness theory
• Mathematical Models and Numerical Methods for Bose-Einstein Condensation
• Multilinear Embedding -- convolution estimates on smooth submanifolds
• Small data global well-posedness for a Boltzmann equation via bilinear spacetime estimates
• Counterexamples to $L^p$ collapsing estimates
• Classical Proofs Of Kato Type Smoothing Estimates for The Schrödinger Equation with Quadratic Potential in R^n+1 with application
• Mean field approximation of many-body quantum dynamics for Bosons in a discrete numerical model
• A new proof of existence of solutions for focusing and defocusing Gross-Pitaevskii hierarchies
• On the integrability of the wave propagator arising from the Liouville-von Neumann equation
• Blowup alternative for Gross-Pitaevskii hierarchies
• On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein Condensate
• Mean field dynamics of a quantum tracer particle interacting with a boson gas
• On the scattering problem for infinitely many fermions in dimensions $d\ge 3$ at positive temperature