Well-Posedness of the Nonlinear Schr\"odinger Equation on the Half-Plane

A. Alexandrou Himonas; Dionyssios Mantzavinos

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arXiv · 1810.02395

Well-Posedness of the Nonlinear Schr\"odinger Equation on the Half-Plane

A. Alexandrou Himonas·Dionyssios Mantzavinos

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Abstract

The initial-boundary value problem (IBVP) for the nonlinear Schr\"odinger (NLS) equation on the half-plane with nonzero boundary data is studied by advancing a novel approach recently developed for the well-posedness of the cubic NLS on the half-line, which takes advantage of the solution formula produced by the unified transform of Fokas for the associated linear IBVP. For initial data in Sobolev spaces on the half-plane and boundary data in Bourgain spaces arising naturally when the linear IBVP is solved with zero initial data, the present work provides a local well-posedness result for NLS initial-boundary value problems in higher dimensions.

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A. Alexandrou Himonas, Dionyssios Mantzavinos. 2018-10-04. Well-Posedness of the Nonlinear Schr\"odinger Equation on the Half-Plane. https://arxiv.org/abs/1810.02395

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