Mass-energy threshold dynamics for the focusing NLS with a repulsive inverse-power potential

2022/02/23 by Alex H. Ardila, Ardila, Alex H., Masaru Hamano +3
Mathematics · Physics and Astronomy · #35P25 #35Q55 #37K45 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Quantum Chromodynamics and Particle Interactions #Spectral Theory in Mathematical Physics #math.AP #msc:35P25 #msc:35Q55 #msc:37K45

paper · pdf · doi:10.48550/arxiv.2202.11640

21 pages

arxiv created 2022/02/23 · openalex publication_date 2022/02/23 · arxiv updated 2022/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study long time dynamics (i.e., scattering and blow-up) of solutions for the focusing NLS with a repulsive inverse-power potential and with initial data lying exactly at the mass-energy threshold, namely, when E_V(u₀)M(u₀)=E₀(Q)M(Q). Moreover, we prove failure of the uniform space-time bounds at the mass-energy threshold.

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