  This work studies the initial-boundary value problem of the two-dimensional
nonlinear Schr\"odinger equation on the half-plane with initial data in Sobolev
spaces and Neumann or Robin boundary data in appropriate Bourgain spaces. It
establishes well-posedness in the sense of Hadamard by utilizing the explicit
solution formula for the forced linear initial-boundary value problem obtained
via Fokas's unified transform, and a contraction mapping argument.
