On the unconditional uniqueness of solutions to the infinite radial Chern-Simons-Schr\"odinger hierarchy

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