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Volume 37, Issue 3
Scattering for the Non-Radial Defocusing Nonlinear Inhomogeneous Hartree Equation

Chengjun Tong, Haigen Wu & Chengbin Xu

DOI: 10.4208/jpde.v37.n3.4

J. Part. Diff. Eq., 37 (2024), pp. 278-294.

Published online: 2024-08

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  • 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.
  • Keywords

Inhomogeneous Hartree equation, scattering theory, Strichartz estimates, Morawetz estimate.

  • AMS Subject Headings

35P25

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JPDE-37-278, author = {Tong , ChengjunWu , Haigen and Xu , Chengbin}, title = {Scattering for the Non-Radial Defocusing Nonlinear Inhomogeneous Hartree Equation}, journal = {Journal of Partial Differential Equations}, year = {2024}, volume = {37}, number = {3}, pages = {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.
}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v37.n3.4}, url = {http://global-sci.org/intro/article_detail/jpde/23343.html} }
TY - JOUR T1 - Scattering for the Non-Radial Defocusing Nonlinear Inhomogeneous Hartree Equation AU - Tong , Chengjun AU - Wu , Haigen AU - Xu , Chengbin JO - Journal of Partial Differential Equations VL - 3 SP - 278 EP - 294 PY - 2024 DA - 2024/08 SN - 37 DO - http://doi.org/10.4208/jpde.v37.n3.4 UR - https://global-sci.org/intro/article_detail/jpde/23343.html KW - Inhomogeneous Hartree equation, scattering theory, Strichartz estimates, Morawetz estimate. AB -
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.
Chengjun Tong, Haigen Wu & Chengbin Xu. (2024). Scattering for the Non-Radial Defocusing Nonlinear Inhomogeneous Hartree Equation. Journal of Partial Differential Equations. 37 (3). 278-294. doi:10.4208/jpde.v37.n3.4
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