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Proceedings of the American Mathematical Society Series B

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Global well-posedness and scattering for the quantum Zakharov system in $ L^2$


Authors: Yung-Fu Fang and Kenji Nakanishi
Journal: Proc. Amer. Math. Soc. Ser. B 6 (2019), 21-32
MSC (2010): Primary 35L30; Secondary 35L05, 35Q55
DOI: https://doi.org/10.1090/bproc/42
Published electronically: June 25, 2019
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Abstract: We study the Cauchy problem for the quantum Zakharov system in the class of square-integrable functions on the Euclidean space of general dimensions. The local well-posedness is proven for dimensions up to eight, together with global existence for dimensions up to five, as well as scattering for small initial data in dimensions greater than three.


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Additional Information

Yung-Fu Fang
Affiliation: Department of Mathematics, National Cheng Kung University, No. 1, Dasyue Road, Tainan City 70101, Taiwan
Email: yffang@mail.ncku.edu.tw

Kenji Nakanishi
Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
Email: kenji@kurims.kyoto-u.ac.jp

DOI: https://doi.org/10.1090/bproc/42
Keywords: quantum Zakharov system, well-posedness, global solutions, scatterng
Received by editor(s): December 23, 2018
Published electronically: June 25, 2019
Additional Notes: The first author was partially supported by MOST, MRPC, and NCTS (Taiwan).
The second author was supported by JSPS KAKENHI Grant Number JP17H02854.
The first author is the corresponding author.
Communicated by: Joachim Krieger
Article copyright: © Copyright 2019 by the author under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)