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On the supercritical Schrödinger equation on the exterior of a ball
Communications in Partial Differential Equations ( IF 2.1 ) Pub Date : 2021-02-10 , DOI: 10.1080/03605302.2021.1881111
Piero D’Ancona 1
Affiliation  

Abstract

We consider the mixed problem on the exterior of the unit ball in Rn,n2, for a defocusing Schrödinger equation with a power nonlinearity |u|p1u, 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.



中文翻译:

关于球外部的超临界薛定谔方程

摘要

我们考虑单元球外部的混合问题 电阻n,n2, 对于具有功率非线性的散焦薛定谔方程 ||-1,零边界数据。假设初始数据是非径向的,径向初始数据的扰动足够小,我们证明对于所有幂>n+6 该解一直存在,其 Sobolev 范数不会膨胀,并且该解在能量类中是唯一的。

更新日期:2021-02-10
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