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Asymptotic integration of Navier-Stokes equations with potential forces. II: An explicit Poincaré-Dulac normal form. (English) Zbl 1232.35115
Summary: 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 [the first and the third author, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 4, 1–47 (1987; Zbl 0635.35075)] 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.

MSC:
35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
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