Well-posedness of the nonlinear Schrödinger equation on the half-plane. (15th September 2020)

• Record Type: Journal Article
• Authors: Himonas, A Alexandrou; Mantzavinos, Dionyssios
• Is Part Of: Nonlinearity. Volume 33:Number 10(2020)
• Page Start: 5567
• Page End: 5609
• Publication Date: 2020-09-15
• Subjects: 2D nonlinear Schrödinger equation -- initial-boundary value problem -- well-posedness in Sobolev spaces -- Bourgain spaces -- unified transform method of Fokas -- linear space-time estimates -- Strichartz estimates; Primary: 35Q55 -- 35G16 -- 35G31; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ab9499
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: The initial-boundary value problem (ibvp) for the nonlinear Schrödinger (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 equation on the half-line, which takes advantage of the solution formula produced via 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 spontaneously when the linear ibvp is solved with zero initial data, the present work introduces a natural method for proving local well-posedness of nonlinear ibvps in higher dimensions.