The focusing cubic NLS on exterior domains in three dimensions

2015/01/21 by Rowan Killip, Monica Vişan, Killip, Rowan +3
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1501.05062

openalex publication_date 2015/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the focusing cubic NLS in the exterior Ω of a smooth, compact, strictly convex obstacle in three dimensions. We prove that the threshold for global existence and scattering is the same as for the problem posed on Euclidean space. Specifically, we prove that if E(u₀)M(u₀)

Citations

• A relation between pointwise convergence of functions and convergence of functionals

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