Asymptotic integrations of Navier-Stokes equations with potential forces. I. (English) Zbl 0739.35066

Foias, C.; Saut, J. C.

Indiana Univ. Math. J. 40, No. 1, 305-320 (1991).

This work may be considered as a continuation of the previous paper of the authors [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 4, 1-47 (1987; Zbl 0635.35075)], where they introduced the normal form of the Navier-Stokes equations. The main purpose of the present work is to derive some new properties of the normal form and of the normalizing mapping. Namely, the authors prove that the normal form is canonical and give a way to compute it explicitly. Also, in the periodic case they determine the inverse of a normalizing map. The methods and results are not only relevant to the Navier-Stokes equations. They can be used for other nonlinear parabolic equations or for ordinary differential equations as well.

Reviewer: Y.R.Romanovsky (Pereslavl-Zalessky)

MSC:

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

Keywords:

properties of the normal form; periodic case; inverse of normalizing map

Citations:

Zbl 0635.35075