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Sbornik: Mathematics, 2005, Volume 196, Issue 1, Pages 29–61
DOI: https://doi.org/10.1070/SM2005v196n01ABEH000871 (Mi sm1260) 		 
This article is cited in 20 scientific papers (total in 20 papers)

Lieb–Thirring integral inequalities and their applications to attractors of the Navier–Stokes equations

A. A. Ilyin

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences
English version PDF (331 kB) Citations (20)
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DOI: https://doi.org/10.1070/SM2005v196n01ABEH000871
Abstract: Integral inequalities of Lieb–Thirring type and their generalizations are proved. All the corresponding constants are given in explicit form. Special attention is devoted to applications to the attractors of the two-dimensional Navier–Stokes equations. In particular, an explicit two-sided estimate of the attractor dimension is established for the Kolmogorov problem on the two-dimensional elongated torus.
Received: 02.02.2004
Russian version:
Matematicheskii Sbornik, 2005, Volume 196, Number 1, Pages 33–66
DOI: https://doi.org/10.4213/sm1260
Bibliographic databases:
UDC: 517.9
MSC: 26D10, 35Q10
Language: English
Original paper language: Russian
Citation: A. A. Ilyin, “Lieb–Thirring integral inequalities and their applications to attractors of the Navier–Stokes equations”, Mat. Sb., 196:1 (2005), 33–66; Sb. Math., 196:1 (2005), 29–61
Citation in format AMSBIB
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    • This publication is cited in the following 20 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    English version PDF:22
    References:74
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