On the supercritical Schrödinger equation on the exterior of a ball

2021/06/30 by Piero DʼAncona, D'Ancona, Piero
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Stability and Controllability of Differential Equations #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2106.16183

openalex publication_date 2021/06/30 · openalex created_date 2021/07/05 · openalex updated_date 2026/07/28

Abstract

We consider the mixed problem on the exterior of the unit ball in ℝⁿ, n≥2, for a defocusing Schrödinger equation with a power nonlinearity |u|^p-1u, with zero boundary data. Assuming that the initial data are non radial, sufficiently small perturbations of large radial initial data, we prove that for all powers p>n+6 the solution exists for all times, its Sobolev norms do not inflate, and the solution is unique in the energy class.

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