کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4591597 | 1335039 | 2011 | 29 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Asymptotic integration of Navier–Stokes equations with potential forces. II. An explicit Poincaré–Dulac normal form Asymptotic integration of Navier–Stokes equations with potential forces. II. An explicit Poincaré–Dulac normal form](/preview/png/4591597.png)
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.
Journal: Journal of Functional Analysis - Volume 260, Issue 10, 15 May 2011, Pages 3007-3035