Scattering Below the Ground State for the 2d Radial Nonlinear Schrödinger Equation
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.
A. K. Arora et al., "Scattering Below the Ground State for the 2d Radial Nonlinear Schrödinger Equation," Proceedings of the American Mathematical Society, vol. 148, no. 4, pp. 1653 - 1663, American Mathematical Society, Apr 2020.
The definitive version is available at https://doi.org/10.1090/proc/14824
Mathematics and Statistics
International Standard Serial Number (ISSN)
Article - Journal
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01 Apr 2020