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Russian Mathematical Surveys, 2004, Volume 59, Issue 2, Pages 297–312
DOI: https://doi.org/10.1070/RM2004v059n02ABEH000719 (Mi rm719) 		 
This article is cited in 24 scientific papers (total in 24 papers)

Passive scalar equation in a turbulent incompressible Gaussian velocity field

S. V. Lototskii, B. L. Rozovskii

University of Southern California
English version PDF (214 kB) Citations (24)
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DOI: https://doi.org/10.1070/RM2004v059n02ABEH000719
Abstract: The time evolution of a passive scalar in a turbulent homogeneous incompressible Gaussian flow is considered. The turbulent nature of the flow results in non-smooth coefficients of the corresponding evolution equation. A strong solution (in the probabilistic sense) of the equation is constructed by using the Wiener Chaos expansion, and properties of the solution are studied. In particular, a certain $L_p$-regularity of the solution and a representation formula of Feynman–Kac type (or a Lagrangian formula) are among the results obtained. The results can be applied to both viscous and conservative flows.
Received: 20.06.2003
Russian version:
Uspekhi Matematicheskikh Nauk, 2004, Volume 59, Issue 2(356), Pages 105–120
DOI: https://doi.org/10.4213/rm719
Bibliographic databases:
Document Type: Article
UDC: 519.218.1
MSC: Primary 60H15, 76F25; Secondary 35R60, 60G15, 76D99, 60G60
Language: English
Original paper language: Russian
Citation: S. V. Lototskii, B. L. Rozovskii, “Passive scalar equation in a turbulent incompressible Gaussian velocity field”, Uspekhi Mat. Nauk, 59:2(356) (2004), 105–120; Russian Math. Surveys, 59:2 (2004), 297–312
Citation in format AMSBIB
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    • This publication is cited in the following 24 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:91
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