Uniqueness of the Leray-Hopf solution for a dyadic model

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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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2017-12, Vol.369 (12), p.8663-8684
Main Author: FILONOV, N. D.
Format: Article
Language:English
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Summary: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.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/6996