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Linearization and normal form of the Navier-Stokes equations with potential forces. (English) Zbl 0635.35075

A normalization theory for the incompressible Navier-Stokes equations with potential body forces is derived by means of a global asymptotic expansion of a solution as time goes to infinity. The normal form is an equation in a suitable Frechet space, whose nonlinear terms correspond to resonances in the spectrum of the Stokes operator. The normalization mapping is globally defined, analytic, one to one. It is also shown that the analogue of this normalization mapping for the Burgers equation can be explicitly computed in terms of the Cole-Hopf transform.
Reviewer: Y.R.Romanovsky

MSC:

35Q30 Navier-Stokes equations
35C20 Asymptotic expansions of solutions to PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
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