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Algebra i Analiz, 2020, Volume 32, Issue 2, Pages 229–253 (Mi aa1695)  
This article is cited in 3 scientific papers (total in 3 papers)

Research Papers

Nonuniqueness of Leray-Hopf solutions for a dyadic model

N. Filonovab, P. A. Khodunovc

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
b Saint Petersburg State University
c Chebyshev Laboratory, St. Petersburg State University, Department of Mathematics and Mechanics
Full-text PDF (285 kB) Citations (3)
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Abstract: The dyadic model $ \dot u_n + \lambda ^{2n}u_n - \lambda ^{\beta n}u_{n-1}^2 + \lambda ^{\beta (n+1)}u_nu_{n+1} = f_n$, $ u_n(0)=0$, is considered. It is shown that in the case of nontrivial right-hand side the system may have two different Leray-Hopf solutions.
Keywords: systems of ordinary differential equations, Navier–Stokes equations, dyadic model, nonuniqueness of solutions.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00099_а
The work was supported by RFBR grant, 17-01-00099-a.
Received: 11.11.2018
English version:
St. Petersburg Mathematical Journal, 2021, Volume 32, Issue 2, Pages 371–387
DOI: https://doi.org/10.1090/spmj/1651
Bibliographic databases:
Document Type: Article
MSC: Primary 35Q30; Secondary 34E05
Language: Russian
Citation: N. Filonov, P. A. Khodunov, “Nonuniqueness of Leray-Hopf solutions for a dyadic model”, Algebra i Analiz, 32:2 (2020), 229–253; St. Petersburg Math. J., 32:2 (2021), 371–387
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и анализ St. Petersburg Mathematical Journal
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