Scattering below the ground state for the intercritical non-radial inhomogeneous NLS. (December 2022)

• Record Type: Journal Article
• Authors: Cardoso, Mykael; Farah, Luiz Gustavo; Guzmán, Carlos M.; Murphy, Jason
• Is Part Of: Nonlinear analysis. Volume 68(2022)
• Publication Date: 2022-12
• Subjects: Inhomogeneous NLS -- Intercritical -- Non-radial data -- Scattering; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103687
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We consider the focusing inhomogeneous nonlinear Schrödinger equation i ∂ t u + Δ u + | x | − b | u | α u = 0 on R × R N, with N ≥ 2, 0 < b < min { N 2, 2 }, and 4 − 2 b N < α < 4 − 2 b N − 2 . These constraints make the equation mass-supercritical and energy-subcritical. We extend the results of Farah and Guzmán (2020) and Miao et al. (2019) and prove scattering below the ground state with general initial data.