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The Robin and Neumann problems for the nonlinear Schrödinger equation on the half-plane (2204.13005v1)
Published 27 Apr 2022 in math.AP
Abstract: 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.