Scattering below the ground state for the 2dd radial nonlinear Schrödinger equation

preprint2019arXivOpen access

Abstract

We revisit the problem of scattering below the ground state threshold for the mass-supercritical focusing nonlinear Schrödinger equation in two space dimensions. We present a simple new proof that treats the case of radial initial data. The key ingredient is a localized virial/Morawetz estimate; the radial assumption aids in controlling the error terms resulting from the spatial localization.

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