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In this article we establish the unconditional uniqueness of solutions to anInfinite Radial Chern-Simons-Schr\"odinger (IRCSS) hierarchy in two spatialdimensions. The IRCSS hierarchy is a system of infinitely many coupled PDEsthat describes the limiting Chern-Simons-Schr\"odinger dynamics of infinitelymany interacting anyons. The anyons are two dimensional objects which interactthrough a self-generated field. Due to the interactions with the self-generatedfield, the IRCSS hierarchy is a system of nonlinear PDEs, which distinguishesit from the linear infinite hierarchies studied previously. Factorizedsolutions of the IRCSS hierarchy are determined by solutions of theChern-Simons-Schr\"odinger system. Our result therefore implies theunconditional uniqueness of solutions to the radial Chern-Simons-Schr\"odingersystem as well.

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