ON THE UNCONDITIONAL UNIQUENESS OF SOLUTIONS TO THE INFINITE RADIAL CHERN-SIMONS-SCHRODINGER HIERARCHY

被引：25

作者：

Chen, Xuwen ^{[1
]}

Smith, Paul ^{[2
]}

机构：

[1] Brown Univ, Dept Math, Providence, RI 02912 USA

[2] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

来源：

ANALYSIS & PDE | 2014年 / 7卷 / 07期

关键词：

Chern-Simons-Schrodinger system; Chern-Simons-Schrodinger hierarchy; unconditional uniqueness; GROSS-PITAEVSKII EQUATION; MEAN-FIELD LIMIT; ELECTRICALLY CHARGED VORTICES; QUANTUM BOLTZMANN-EQUATION; RIGOROUS DERIVATION; VORTEX SOLITONS; DYNAMICS; BOSONS; EVOLUTION;

D O I：

10.2140/apde.2014.7.1683

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we establish the unconditional uniqueness of solutions to an infinite radial Chern-Simons-Schrodinger (IRCSS) hierarchy in two spatial dimensions. The IRCSS hierarchy is a system of infinitely many coupled PDEs that describes the limiting Chern-Simons-Schrodinger 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-Schrodinger system. Our result therefore implies the unconditional uniqueness of solutions to the radial Chern-Simons-Schrodinger system as well.

引用

页码：1683 / 1712

页数：30

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