On the unconditional uniqueness of solutions to the infinite radial Chern-Simons-Schrödinger hierarchy

Abstract

In this article we establish the unconditional uniqueness of solutions to an Infinite Radial Chern-Simons-Schrödinger (IRCSS) hierarchy in two spatial dimensions. The IRCSS hierarchy is a system of infinitely many coupled PDEs that describes the limiting Chern-Simons-Schrödinger dynamics of infinitely many interacting anyons. The anyons are two dimensional objects which interact through a self-generated field. Due to the interactions with the self-generated field, the IRCSS hierarchy is a system of nonlinear PDEs, which distinguishes it from the linear infinite hierarchies studied previously. Factorized solutions of the IRCSS hierarchy are determined by solutions of the Chern-Simons-Schrödinger system. Our result therefore implies the unconditional uniqueness of solutions to the radial Chern-Simons-Schrödinger system as well.

arXiv commentRevised according to the referee report. Accepted to appear in Analysis & PDE

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• The Derivation of the ${\mathbb{T}}^3$ Energy-critical NLS from Quantum Many-body Dynamics
• Randomization and the Gross-Pitaevskii hierarchy
• Focusing Quantum Many-body Dynamics II: The Rigorous Derivation of the 1D Focusing Cubic Nonlinear Schrödinger Equation from 3D
• The Gross-Pitaevskii hierarchy on general rectangular tori
• 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
• The Unconditional Uniqueness for the Energy-critical Nonlinear Schrödinger Equation on ${\mathbb{T}}^4$
• Uniqueness of solutions to the 3D quintic Gross-Pitaevskii Hierarchy
• Well/ill-posedness bifurcation for the Boltzmann equation with constant collision kernel
• On the mean-field and semiclassical limit from quantum $N$-body dynamics