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Scattering below the ground state for the 2$d$ radial nonlinear Schr\"odinger equation

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arxiv 1906.00515 v1 pith:CPDEMM4K submitted 2019-06-03 math.AP

Anudeep Kumar Arora , Benjamin Dodson , Jason Murphy This is my paper · ORCID
classification math.AP
keywords radialbelowequationgroundnonlinearodingerscatteringschr
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We revisit the problem of scattering below the ground state threshold for the mass-supercritical focusing nonlinear Schr\"odinger 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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  1. Energy scattering for a class of inhomogeneous nonlinear Schr\"odinger equation in two dimensions

    math.AP 2019-08 accept novelty 5.0 of 10

    For the 2D inhomogeneous NLS with 0<b<1 and α>2-b, radial H^1 solutions scatter in both focusing (below ground state) and defocusing cases.

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