Asymptotic integration of Navier–Stokes equations with potential forces. II. An explicit Poincaré–Dulac normal form
| Autor: | Luan Hoang, Ciprian Foias, Jean-Claude Saut |
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| Rok vydání: | 2011 |
| Předmět: |
Body force
Normalization (statistics) Formal power series 010102 general mathematics Mathematical analysis Poincaré–Dulac normal form Non-dimensionalization and scaling of the Navier–Stokes equations 01 natural sciences 010101 applied mathematics Sobolev space Nonlinear system Navier–Stokes equations Homogeneous gauge Linearization Nonlinear dynamics 0101 mathematics Analysis Mathematics |
| Zdroj: | Journal of Functional Analysis. 260(10):3007-3035 |
| ISSN: | 0022-1236 |
| DOI: | 10.1016/j.jfa.2011.02.005 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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