Well-posedness of the nonlinear Schrödinger equation on the half-plane

DOI10.1088/1361-6544/ab9499zbMath1452.35188arXiv1810.02395OpenAlexW3160922718MaRDI QIDQ5136502

A. Alexandrou Himonas, Dionyssios Mantzavinos

Publication date: 26 November 2020

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.02395

zbMATH Keywords

initial-boundary value problem2D nonlinear Schrödinger equationStrichartz estimatesBourgain spaceswell-posedness in Sobolev spaceslinear space-time estimatesunified transform method of Fokas

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Initial-boundary value problems for linear higher-order PDEs (35G16) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Initial-boundary value problems for nonlinear higher-order PDEs (35G31)

Related Items (14)

The interior-boundary Strichartz estimate for the Schrödinger equation on the half-line revisited ⋮ The Korteweg-de Vries equation on the half-line with Robin and Neumann data in low regularity spaces ⋮ A higher dispersion KdV equation on the half-line ⋮ Dispersion estimates for the boundary integral operator associated with the fourth order Schrödinger equation posed on the half line ⋮ Boundary behavior for the heat equation on the half‐line ⋮ The Majda-Biello system on the half-line ⋮ Integral representations for the double-diffusivity system on the half-line ⋮ The linear Lugiato-Lefever equation with forcing and nonzero periodic or nonperiodic boundary conditions ⋮ Low regularity well-posedness for dispersive equations on semi-infinite intervals ⋮ The nonlinear Schrödinger equation on the half-line with a Robin boundary condition ⋮ Fokas method for linear boundary value problems involving mixed spatial derivatives ⋮ The initial-boundary value problem for the biharmonic Schrödinger equation on the half-line ⋮ The Neumann and Robin problems for the Korteweg–de Vries equation on the half-line ⋮ Extended water wave systems of Boussinesq equations on a finite interval: theory and numerical analysis

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