Well-posedness for the Cubic Nonlinear Schrödinger Equation With Nonlinearity Supported on a Hypersurface

Xilin Chen; Jianlei Huang

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arXiv · 2610.32180

Well-posedness for the Cubic Nonlinear Schrödinger Equation With Nonlinearity Supported on a Hypersurface

Xilin Chen·Jianlei Huang

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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.

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BibTeX RIS

Xilin Chen, Jianlei Huang. 2026-10-23. Well-posedness for the Cubic Nonlinear Schrödinger Equation With Nonlinearity Supported on a Hypersurface. https://arxiv.org/abs/2610.32180

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