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Russian Mathematical Surveys, 2000, Volume 55, Issue 4, Pages 635–666
DOI: https://doi.org/10.1070/rm2000v055n04ABEH000313 (Mi rm313) 		 
This article is cited in 23 scientific papers (total in 23 papers)

Recent results on mathematical and statistical hydrodynamics

W. Ea, Ya. G. Sinaibc

a Courant Institute of Mathematical Sciences
b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
c Princeton University, Department of Mathematics
English version PDF (746 kB) Citations (23)
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DOI: https://doi.org/10.1070/rm2000v055n04ABEH000313
Abstract: This paper is a survey of recent results of the authors and their collaborators on stochastic partial differential equations in hydrodynamics. We discuss the stochastic Burgers equation, the stochastic Navier–Stokes equation, and the stochastic passive scalar transport equation. In contrast to previous publications on this subject (see, for example, [25], which is mainly devoted to existence problems for stochastic dynamics), the work surveyed here emphasizes qualitative properties of solutions, including the existence and uniqueness of an invariant measure under certain physical assumptions, the asymptotic behaviour of the statistics of these solutions, and so on. We also discuss new investigations concerning the deterministic Navier–Stokes equation.
Received: 03.04.2000
Russian version:
Uspekhi Matematicheskikh Nauk, 2000, Volume 55, Issue 4(334), Pages 25–58
DOI: https://doi.org/10.4213/rm313
Bibliographic databases:
Document Type: Article
UDC: 517.95+519.21
MSC: Primary 35R60, 35Q53, 35Q30; Secondary 35L67, 76D03, 76D05, 76N10, 60H15
Language: English
Original paper language: Russian
Citation: W. E, Ya. G. Sinai, “Recent results on mathematical and statistical hydrodynamics”, Uspekhi Mat. Nauk, 55:4(334) (2000), 25–58; Russian Math. Surveys, 55:4 (2000), 635–666
Citation in format AMSBIB
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    • This publication is cited in the following 23 articles:
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    		Успехи математических наук Russian Mathematical Surveys
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