Invariant Gibbs dynamics for the nonlinear Schrödinger equations on the disc

We consider the two-dimensional defocusing nonlinear Schrödinger equation (NLS) on the unit disc in the plane with the Gibbs initial data under radial symmetry. By using a type of random averaging operator ansatz, we build a strong local-in-time solution theory, and thus prove almost sure global well-posedness and invariance of the Gibbs measure via Bourgain’s invariant measure argument. This work completes the program initiated by Tzvetkov (2006, 2008) on the construction of invariant Gibbs dynamics (of strong solutions) for NLS on the disc.