Scattering in H¹ for the Intercritical NLS with an Inverse-Square Potential
We study the nonlinear Schrödinger equation with an inverse-square potential in dimensions 3 ≤ d ≤ 6. We consider both focusing and defocusing nonlinearities in the mass-supercritical and energy-subcritical regime. In the focusing case, we prove a scattering/blowup dichotomy below the ground state. In the defocusing case, we prove scattering in H1 for arbitrary data.
J. Lu et al., "Scattering in H¹ for the Intercritical NLS with an Inverse-Square Potential," Journal of Differential Equations, vol. 264, no. 5, pp. 3174-3211, Academic Press Inc., Mar 2018.
The definitive version is available at https://doi.org/10.1016/j.jde.2017.11.015
Mathematics and Statistics
Keywords and Phrases
Inverse-square potential; Nonlinear Schrödinger equation; Scattering
International Standard Serial Number (ISSN)
Article - Journal
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