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

作者：Foias Ciprian; Hoang Luan^*; Saut Jean Claude

来源：Journal of Functional Analysis, 2011, 260(10): 3007-3035.

DOI：10.1016/j.jfa.2011.02.005

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

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. Poincare Anal. Non Lineaire 4 (1) (1987) 1-47], produces a Poincare-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.

• 出版日期2011-5-15