Properties of time-dependent statistical solutions of the three-dimensional Navier-Stokes equations

Ciprian Foias[1]; Ricardo M. S. Rosa[2]; Roger Temam[3]

  • [1] Texas A&M University Department of Mathematics College Station, TX 77843 (USA)
  • [2] Universidade Federal do Rio de Janeiro Instituto de Matemática Caixa Postal 68530 Ilha do Fundão Rio de Janeiro, RJ 21945-970 (Brazil)
  • [3] Indiana University Department of Mathematics Bloomington, IN 47405 (USA)

Annales de l’institut Fourier (2013)

  • Volume: 63, Issue: 6, page 2515-2573
  • ISSN: 0373-0956

Abstract

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This work is devoted to the concept of statistical solution of the Navier-Stokes equations, proposed as a rigorous mathematical object to address the fundamental concept of ensemble average used in the study of the conventional theory of fully developed turbulence. Two types of statistical solutions have been proposed in the 1970’s, one by Foias and Prodi and the other one by Vishik and Fursikov. In this article, a new, intermediate type of statistical solution is introduced and studied. This solution is a particular type of a statistical solution in the sense of Foias and Prodi which is constructed in a way akin to the definition given by Vishik and Fursikov, in such a way that it possesses a number of useful analytical properties.

How to cite

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Foias, Ciprian, Rosa, Ricardo M. S., and Temam, Roger. "Properties of time-dependent statistical solutions of the three-dimensional Navier-Stokes equations." Annales de l’institut Fourier 63.6 (2013): 2515-2573. <http://eudml.org/doc/275649>.

@article{Foias2013,
abstract = {This work is devoted to the concept of statistical solution of the Navier-Stokes equations, proposed as a rigorous mathematical object to address the fundamental concept of ensemble average used in the study of the conventional theory of fully developed turbulence. Two types of statistical solutions have been proposed in the 1970’s, one by Foias and Prodi and the other one by Vishik and Fursikov. In this article, a new, intermediate type of statistical solution is introduced and studied. This solution is a particular type of a statistical solution in the sense of Foias and Prodi which is constructed in a way akin to the definition given by Vishik and Fursikov, in such a way that it possesses a number of useful analytical properties.},
affiliation = {Texas A&M University Department of Mathematics College Station, TX 77843 (USA); Universidade Federal do Rio de Janeiro Instituto de Matemática Caixa Postal 68530 Ilha do Fundão Rio de Janeiro, RJ 21945-970 (Brazil); Indiana University Department of Mathematics Bloomington, IN 47405 (USA)},
author = {Foias, Ciprian, Rosa, Ricardo M. S., Temam, Roger},
journal = {Annales de l’institut Fourier},
keywords = {Navier-Stokes equations; statistical solutions; turbulence; measure theory; functional analysis},
language = {eng},
number = {6},
pages = {2515-2573},
publisher = {Association des Annales de l’institut Fourier},
title = {Properties of time-dependent statistical solutions of the three-dimensional Navier-Stokes equations},
url = {http://eudml.org/doc/275649},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Foias, Ciprian
AU - Rosa, Ricardo M. S.
AU - Temam, Roger
TI - Properties of time-dependent statistical solutions of the three-dimensional Navier-Stokes equations
JO - Annales de l’institut Fourier
PY - 2013
PB - Association des Annales de l’institut Fourier
VL - 63
IS - 6
SP - 2515
EP - 2573
AB - This work is devoted to the concept of statistical solution of the Navier-Stokes equations, proposed as a rigorous mathematical object to address the fundamental concept of ensemble average used in the study of the conventional theory of fully developed turbulence. Two types of statistical solutions have been proposed in the 1970’s, one by Foias and Prodi and the other one by Vishik and Fursikov. In this article, a new, intermediate type of statistical solution is introduced and studied. This solution is a particular type of a statistical solution in the sense of Foias and Prodi which is constructed in a way akin to the definition given by Vishik and Fursikov, in such a way that it possesses a number of useful analytical properties.
LA - eng
KW - Navier-Stokes equations; statistical solutions; turbulence; measure theory; functional analysis
UR - http://eudml.org/doc/275649
ER -

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