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

This article is cited in 11 scientific papers (total in 11 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
    9. Pourhadi E., Khrennikov A., Saadati R., Oleschko K., Correa Lopez Maria de Jesus, “Solvability of the P-Adic Analogue of Navier-Stokes Equation Via the Wavelet Theory”, Entropy, 21:11 (2019), 1129  crossref  mathscinet  isi
    10. Pourhadi E., Khrennikov A.Yu., Oleschko K., Lopez Maria de Jesus Correa, “Solving Nonlinearp-Adic Pseudo-Differential Equations: Combining the Wavelet Basis With the Schauder Fixed Point Theorem”, J. Fourier Anal. Appl., 26:4 (2020), 70  crossref  mathscinet  isi
    11. Antoniouk V A., Khrennikov A.Yu., Kochubei A.N., “Multidimensional Nonlinear Pseudo-Differential Evolution Equation With P-Adic Spatial Variables”, J. Pseudo-Differ. Oper. Appl., 11:1 (2020), 311–343  crossref  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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