Properties of Stationary Statistical Solutions of the Three-Dimensional Navier–Stokes Equations

  • Ciprian Foias
  • Ricardo M. S. RosaEmail author
  • Roger M. Temam


The stationary version of a modified definition of statistical solution for the three-dimensional incompressible Navier–Stokes equations introduced in a previous work is investigated. Particular types of such stationary statistical solutions and their analytical properties are addressed. Results on the support and carriers of these stationary statistical solutions are also given, showing in particular that they are supported on the weak global attractor and are carried by a more regular part of the weak global attractor containing Leray–Hopf weak solutions which are locally strong solutions. Two recurrence-type results related to these measures are also proved.


Navier–Stokes equations Stationary statistical solutions Accretive measures Recurrence 

Mathematics Subject Classification

35Q30 76D06 76D06 37A05 37L40 37B20 



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Authors and Affiliations

  1. 1.Department of MathematicsTexas A&M UniversityCollege StationUSA
  2. 2.Instituto de MatemáticaUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil
  3. 3.Department of MathematicsIndiana UniversityBloomingtonUSA

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