On the solutions to the normal form of the Navier-Stokes equations

Ciprian Foias, Luan Hoang, Eric Olson, Mohammed Ziane

Research output: Contribution to journalArticle

20 Scopus citations

Abstract

We introduce a construction of regular solutions to the Navier-Stokes equations that is specifically designed for the study of their asymptotic expansions. Using this construction, we give sufficient conditions for the convergence of those expansions. We also construct suitable normed spaces in which they converge. Moreover, in these spaces, the normal form of the Navier-Stokes equations associated with the terms of the asymptotic expansions [9] is a well-behaved infinite system of differential equations. Indiana University Mathematics Journal

Original languageEnglish
Pages (from-to)631-686
Number of pages56
JournalIndiana University Mathematics Journal
Volume55
Issue number2
DOIs
StatePublished - 2006

Keywords

  • Fluid mechanics
  • Navier-Stokes equations
  • Non-linear dynamics
  • Normal forms

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