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Navier and Stokes meet Poincar\''e and Dulac
Keywords:Navier-Stokes, asymptotic expansion, Poincar\''e-Dulac, normal form, normalization map
Abstract:
      This paper surveys various precise (long-time) asymptotic results for the solutions of the Navier-Stokes equations with potential forces in bounded domains. It turns out that the asymptotic expansion leads surprisingly to a kind of Poincar\''e-Dulac normal form of the Navier-Stokes equations. We will also discuss some related results and a few open issues.