Scattering Below the Ground State for the Intercritical Non-Radial Inhomogeneous NLS

Mykael Cardoso; Luiz Gustavo Farah; Carlos M. Guzmán; Jason Murphy

doi:10.1016/j.nonrwa.2022.103687

Scattering Below the Ground State for the Intercritical Non-Radial Inhomogeneous NLS

Mykael Cardoso
, Luiz Gustavo Farah
, Carlos M. Guzmán
, Jason Murphy

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the focusing inhomogeneous nonlinear Schrödinger equation i∂ _t u+Δu+|x| ^-b |u| ^α u=0 on R x R ^N ,with N≥2, 0 < b < min {N/2, 2}, and (4-2b)/N < α < (4-2b)/(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.

Original language	American English
Journal	Nonlinear Analysis: Real World Applications
Volume	68
DOIs	https://doi.org/10.1016/j.nonrwa.2022.103687
State	Published - Dec 1 2022

Keywords

Inhomogeneous NLS
Intercritical
Non-Radial Data
Scattering

Disciplines

Physical Sciences and Mathematics

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https://doi.org/10.1016/j.nonrwa.2022.103687

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title = "Scattering Below the Ground State for the Intercritical Non-Radial Inhomogeneous NLS",

abstract = " We consider the focusing inhomogeneous nonlinear Schr{\"o}dinger equation i∂ t u+Δu+|x| -b |u| α u=0 on R x R N ,with N≥2, 0 < b < min \{N/2, 2\}, and (4-2b)/N < α < (4-2b)/(N-2). These constraints make the equation mass-supercritical and energy-subcritical. We extend the results of Farah and Guzm{\'a}n (2020) and Miao et al. (2019) and prove scattering below the ground state with general initial data.",

keywords = "Inhomogeneous NLS, Intercritical, Non-Radial Data, Scattering",

author = "Mykael Cardoso and Farah, \{Luiz Gustavo\} and Guzm{\'a}n, \{Carlos M.\} and Jason Murphy",

year = "2022",

month = dec,

day = "1",

doi = "10.1016/j.nonrwa.2022.103687",

language = "American English",

volume = "68",

journal = "Nonlinear Analysis: Real World Applications",

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TY - JOUR

T1 - Scattering Below the Ground State for the Intercritical Non-Radial Inhomogeneous NLS

AU - Cardoso, Mykael

AU - Farah, Luiz Gustavo

AU - Guzmán, Carlos M.

AU - Murphy, Jason

PY - 2022/12/1

Y1 - 2022/12/1

N2 - We consider the focusing inhomogeneous nonlinear Schrödinger equation i∂ t u+Δu+|x| -b |u| α u=0 on R x R N ,with N≥2, 0 < b < min {N/2, 2}, and (4-2b)/N < α < (4-2b)/(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.

AB - We consider the focusing inhomogeneous nonlinear Schrödinger equation i∂ t u+Δu+|x| -b |u| α u=0 on R x R N ,with N≥2, 0 < b < min {N/2, 2}, and (4-2b)/N < α < (4-2b)/(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.

KW - Inhomogeneous NLS

KW - Intercritical

KW - Non-Radial Data

KW - Scattering

UR - https://scholarsmine.mst.edu/math_stat_facwork/1115

UR - https://doi.org/10.1016/j.nonrwa.2022.103687

U2 - 10.1016/j.nonrwa.2022.103687

DO - 10.1016/j.nonrwa.2022.103687

M3 - Article

VL - 68

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

ER -

Scattering Below the Ground State for the Intercritical Non-Radial Inhomogeneous NLS

Abstract

Keywords

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