Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on \R

2006/12/15 by J. Colliander, Justin Holmer, Colliander, J. +7 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Nonlinear Waves and Solitons #math.AP

paper · pdf · doi:10.48550/arxiv.math/0612452

arxiv created 2006/12/15 · openalex publication_date 2006/12/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Cauchy problem for a family of semilinear defocusing Schrödinger equations with monomial nonlinearities in one space dimension. We establish global well-posedness and scattering. Our analysis is based on a four-particle interaction Morawetz estimate giving a priori L⁸_t,x spacetime control on solutions.

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• Bilinear virial identities and applications

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