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2014 On the unconditional uniqueness of solutions to the infinite radial Chern–Simons–Schrödinger hierarchy
Xuwen Chen, Paul Smith
Anal. PDE 7(7): 1683-1712 (2014). DOI: 10.2140/apde.2014.7.1683

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 that 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.

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Xuwen Chen. Paul Smith. "On the unconditional uniqueness of solutions to the infinite radial Chern–Simons–Schrödinger hierarchy." Anal. PDE 7 (7) 1683 - 1712, 2014. https://doi.org/10.2140/apde.2014.7.1683

Information

Received: 10 June 2014; Revised: 7 August 2014; Accepted: 10 September 2014; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1307.35273
MathSciNet: MR3293448
Digital Object Identifier: 10.2140/apde.2014.7.1683

Subjects:
Primary: 35A02 , 35Q55 , 81V70
Secondary: 35A23 , 35B45

Keywords: Chern–Simons–Schrödinger hierarchy , Chern–Simons–Schrödinger system , unconditional uniqueness

Rights: Copyright © 2014 Mathematical Sciences Publishers

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