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Uniqueness of the Leray-Hopf solution for a dyadic model


Author: N. D. Filonov
Journal: Trans. Amer. Math. Soc. 369 (2017), 8663-8684
MSC (2010): Primary 34G20; Secondary 35Q30
DOI: https://doi.org/10.1090/tran/6996
Published electronically: March 31, 2017
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Abstract: The dyadic problem $ \dot u_n + \lambda ^{2n} u_n - \lambda ^{\beta n} u_{n-1}^2 + \lambda ^{\beta (n+1)} u_n u_{n+1} = 0$ with ``smooth'' initial data is considered. The uniqueness of the Leray-Hopf solution is proved.


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Additional Information

N. D. Filonov
Affiliation: St. Petersburg Department of Steklov Mathematical Institute, 27 Fontanka, St. Petersburg 191023, Russia — and — Department of Physics, St. Petersburg State University, Ulyanovskaya 1, Petrodvorets, St. Petersburg 198504, Russia
Email: filonov@pdmi.ras.ru

DOI: https://doi.org/10.1090/tran/6996
Received by editor(s): February 13, 2016
Published electronically: March 31, 2017
Additional Notes: The author was supported by grant RFBR 14-01-00306
Article copyright: © Copyright 2017 American Mathematical Society

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