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Scattering for the Non-Radial Defocusing Nonlinear Inhomogeneous Hartree Equation

Scattering for the Non-Radial Defocusing Nonlinear Inhomogeneous Hartree Equation
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Year:    2024

Author:    Chengjun Tong, Haigen Wu, Chengbin Xu

Journal of Partial Differential Equations, Vol. 37 (2024), Iss. 3 : pp. 278–294

Abstract

The purpose of this paper is to study scattering theory for the energy subcritical solutions to the non-radial defocusing inhomogeneous Hartree equation $$i\partial_tu+\Delta u=(I_\alpha\ast|\cdot|^b|u|^{p})|\cdot|^b|u|^{p-2}u.$$ Taking advantage of the decay factor in the nonlinearity instead of the embedding theorem, we establish the scattering criterion for the equation. Together with the Morawetz estimate, we obtain the scattering theory for the energy-subcritical case.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jpde.v37.n3.4

Journal of Partial Differential Equations, Vol. 37 (2024), Iss. 3 : pp. 278–294

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Inhomogeneous Hartree equation scattering theory Strichartz estimates Morawetz estimate.

Author Details

Chengjun Tong

Haigen Wu

Chengbin Xu