Well-posedness for the Cubic Nonlinear Schrödinger Equation With Nonlinearity Supported on a Hypersurface
Year: 2026
Type: preprint
Abstract: We prove that the 2-d cubic nonlinear Schrödinger equation with nonlinearity supported on a line or a sphere is globally well-posed in \(H^1(\mathbb{R}^2)\). For higher dimensions, we prove that the equation with hyperplane-supported nonlinearity is locally well-posed in suitable anisotropic Sobolev spaces. We also prove that the equation with sphere-supported nonlinearity is globally well-posed in \(H^1(\mathbb{R}^n)\) for radial data.
Source: arXiv (Cornell University)
Authors: Chen, Xilin, Huang, Jianlei
Institution: Georgetown University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223708917