Asymptotic integration of Navier-Stokes equations with potential forces. II. An explicit Poincaré-Dulac normal form

Ciprian Foias, Luan Hoang, Jean Claude Saut

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

We study the incompressible Navier-Stokes equations with potential body forces on the three-dimensional torus. We show that the normalization introduced in the paper [C. Foias, J.-C. Saut, Linearization and normal form of the Navier-Stokes equations with potential forces, Ann. Inst. H. Poincaré Anal. Non Linéaire 4 (1) (1987) 1-47], produces a Poincaré-Dulac normal form which is obtained by an explicit change of variable. This change is the formal power series expansion of the inverse of the normalization map. Each homogeneous term of a finite degree in the series is proved to be well-defined in appropriate Sobolev spaces and is estimated recursively by using a family of homogeneous gauges which is suitable for estimating homogeneous polynomials in infinite dimensional spaces.

Original languageEnglish
Pages (from-to)3007-3035
Number of pages29
JournalJournal of Functional Analysis
Volume260
Issue number10
DOIs
StatePublished - May 15 2011

Keywords

  • Homogeneous gauge
  • Navier-Stokes equations
  • Nonlinear dynamics
  • Poincaré-Dulac normal form

Fingerprint Dive into the research topics of 'Asymptotic integration of Navier-Stokes equations with potential forces. II. An explicit Poincaré-Dulac normal form'. Together they form a unique fingerprint.

  • Cite this