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TMF, 2008, Volume 157, Number 3, Pages 413–424 (Mi tmf6289)  

This article is cited in 8 scientific papers (total in 8 papers)

Toward an ultrametric theory of turbulence

S. V. Kozyrev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We discuss the relation between ultrametric analysis, wavelet theory, and cascade models of turbulence. We construct explicit solutions of the nonlinear ultrametric integral equation with quadratic nonlinearity, using a recursive hierarchical procedure analogous to the procedure used for the cascade models of turbulence.

Keywords: ultrametric wavelet, ultrametric analysis, cascade model of turbulence

DOI: https://doi.org/10.4213/tmf6289

Full text: PDF file (457 kB)
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English version:
Theoretical and Mathematical Physics, 2008, 157:3, 1713–1722

Bibliographic databases:

Received: 17.03.2008

Citation: S. V. Kozyrev, “Toward an ultrametric theory of turbulence”, TMF, 157:3 (2008), 413–424; Theoret. and Math. Phys., 157:3 (2008), 1713–1722

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v157/i3/p413

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. V. Kozyrev, “Methods and Applications of Ultrametric and $p$-Adic Analysis: From Wavelet Theory to Biophysics”, Proc. Steklov Inst. Math., 274, suppl. 1 (2011), S1–S84  mathnet  crossref  crossref  zmath  isi  elib
    2. Albeverio S., Khrennikov A.Yu., Shelkovich V.M., “The Cauchy problems for evolutionary pseudo-differential equations over p-adic field and the wavelet theory”, J Math Anal Appl, 375:1 (2011), 82–98  crossref  mathscinet  zmath  isi  elib  scopus
    3. V. M. Shelkovich, “$p$-adic evolution pseudo-differential equations and $p$-adic wavelets”, Izv. Math., 75:6 (2011), 1249–1278  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Kozyrev S.V., Khrennikov A.Yu., “$p$-Adic integral operators in wavelet bases”, Dokl. Math., 83:2 (2011), 209–212  crossref  mathscinet  zmath  isi  elib  elib  scopus
    5. S. V. Kozyrev, A. Yu. Khrennikov, V. M. Shelkovich, “$p$-Adic wavelets and their applications”, Proc. Steklov Inst. Math., 285 (2014), 157–196  mathnet  crossref  crossref  isi  elib  elib
    6. Rachid S., “Stable Random Field With P-Adic-Time and Spectral Density Estimation”, 2015 International Conference on Electrical and Electronics: Techniques and Applications (Eeta 2015), Destech Publications, Inc, 2015, 273–279  isi
    7. Oleschko K., Khrennikov A., “Transport Through a Network of Capillaries From Ultrametric Diffusion Equation With Quadratic Nonlinearity”, Russ. J. Math. Phys., 24:4 (2017), 505–516  crossref  mathscinet  zmath  isi  scopus  scopus
    8. Dragovich B. Khrennikov A.Yu. Kozyrev S.V. Volovich I.V. Zelenov E.I., “P-Adic Mathematical Physics: the First 30 Years”, P-Adic Numbers Ultrametric Anal. Appl., 9:2 (2017), 87–121  crossref  mathscinet  zmath  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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