The normal form of the Navier-Stokes equations in suitable normed spaces

Ciprian Foias, Luan Hoang, Eric Olson, Mohammed Ziane

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


We consider solutions to the incompressible Navier-Stokes equations on the periodic domain Ω = [0, 2 π]3 with potential body forces. Let R ⊆ H1 (Ω)3 denote the set of all initial data that lead to regular solutions. Our main result is to construct a suitable Banach space SA{star operator} such that the normalization map W : R → SA{star operator} is continuous, and such that the normal form of the Navier-Stokes equations is a well-posed system in all of SA{star operator}. We also show that SA{star operator} may be seen as a subset of a larger Banach space V{star operator} and that the extended Navier-Stokes equations, which are known to have global solutions, are well-posed in V{star operator}.

Original languageEnglish
Pages (from-to)1635-1673
Number of pages39
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Issue number5
StatePublished - 2009


  • Asymptotic expansion
  • Long time dynamics
  • Navier-Stokes equations
  • Normal form
  • Normalization map


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