NAVIER AND STOKES MEET POINCAR&#201;AND DULAC

Ciprian Foias; Luan Hoang; Jean-Claude Saut

doi:10.11948/2018.727

2018 Volume 8 Issue 3

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Ciprian Foias, Luan Hoang, Jean-Claude Saut. NAVIER AND STOKES MEET POINCARÉAND DULAC[J]. Journal of Applied Analysis & Computation, 2018, 8(3): 727-763. doi: 10.11948/2018.727

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Ciprian Foias, Luan Hoang, Jean-Claude Saut. NAVIER AND STOKES MEET POINCARÉAND DULAC[J]. Journal of Applied Analysis & Computation, 2018, 8(3): 727-763. doi: 10.11948/2018.727

NAVIER AND STOKES MEET POINCARÉAND DULAC

1 Department of Mathematics, Mailstop 3368, Texas A & M University, College Station, TX 77843-3368, USA;
2 Department of Mathematics and Statistics, Texas Tech University, Box 41042, Lubbock, TX 79409-1042, USA;
3 Laboratoire de Mathématiques d'Orsay, Univ. Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay, France

Abstract

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 Poincaré-Dulac normal form of the Navier-Stokes equations. We will also discuss some related results and a few open issues.
- Navier-Stokes /
- asymptotic expansion /
- Poincaré-Dulac /
- normal form /
- normalization map
MSC: 35C20;35Q30;37G05;37L10;37L25;76D05

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References

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