On the supercritical Schrödinger equation on the exterior of a ball

Abstract

We consider the mixed problem on the exterior of the unit ball in ${\mathbb{R}}^n$, $n\ge 2$, for a defocusing Schrödinger equation with a power nonlinearity $|u{|}^{p-1}u$, with zero boundary data. Assuming that the initial data are non radial, sufficiently small perturbations of \emph{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.

References in corpus (1)

• On the supercritical defocusing NLW outside a ball