Global attractors for the three-dimensional Navier-Stokes equations

George R. Sell

Research output: Contribution to journalArticlepeer-review

183 Scopus citations


In this paper we show that the weak solutions of the Navier-Stokes equations on any bounded, smooth three-dimensional domain have a global attractor for any positive value of the viscosity. The proof of this result, which bypasses the two issues of the possible nonuniqueness of the weak solutions and the possible lack of global regularity of the strong solutions, is based on a new point of view for the construction of the semiflow generated by these equations. We also show that, under added assumptions, this global attractor consists entirely of strong solutions.

Original languageEnglish (US)
Pages (from-to)1-33
Number of pages33
JournalJournal of Dynamics and Differential Equations
Issue number1
StatePublished - 1996


  • Attractor
  • Global attractor
  • Navier-Stokes equations
  • Weak solution


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