Non-dispersive vanishing and blow up at infinity for the energy critical nonlinear Schrödinger equation in R³

2012/12/30 by Cecilia Ortoleva, Galina Perelman, Ortoleva, Cecilia +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1212.6719

openalex publication_date 2012/12/30 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We consider the energy critical focusing NLS in R³ and prove, for any ν sufficiently small, the existence of radial finite energy solutions that as t→∞ behave as a sum of a dynamically rescaled ground state plus a radiation, the scaling law being of the form t^ν.

Citations

• Stable manifolds for all monic supercritical NLS in one dimension

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