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Scattering for a Radial Defocusing Inhomogeneous Choquard Equation

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Abstract

This work considers the long time behavior of the solutions \(u\in C(\mathbb{R},H^{1})\) to the attractive Hartree equation

$$ i\dot{u}+\Delta u=(I_{\alpha }*|\cdot |^{-\gamma }|u|^{p})|x|^{-\gamma }|u|^{p-2}u. $$

Indeed, using a classical Morawetz estimate, the scattering of radial global solutions is proved in \(L^{2}\)-super-critical and \(H^{1}\)-sub-critical regimes.

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Acknowledgements

This work is partially supported by NSF of Gansu Province (China) (Nos. 20JR5RA498, 21JR7RE176), Innovation Ability Promotion Foundation of Universities in Gansu Province (No. 2020B-185) and Tianshui Normal University Research Foundation (ZDY2020-13).

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Authors and Affiliations

  1. Department of Mathematics, College of Science and Arts in Uglat Asugour, Qassim University, Buraydah, Kingdom of Saudi Arabia

    Tarek Saanouni

  2. Faculty of Science of Tunis, LR03ES04 partial differential Equations and applications, University of Tunis El Manar, 2092, Tunis, Tunisia

    Tarek Saanouni

  3. School of Mathematics and Statistics, Tianshui Normal University, Tianshui, 741000, China

    Congming Peng

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  1. Tarek Saanouni
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  2. Congming Peng
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Correspondence to Tarek Saanouni.

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Saanouni, T., Peng, C. Scattering for a Radial Defocusing Inhomogeneous Choquard Equation. Acta Appl Math 177, 6 (2022). https://doi.org/10.1007/s10440-022-00467-0

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