@article{caeedeadc69c40149d599acf1fdbf36c,
title = "Navier and stokes meet poincar{\'e} and dulac",
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.",
keywords = "Asymptotic expansion, Navier-Stokes, Normal form, Normalization map, Poincar{\'e}-Dulac",
author = "Ciprian Foias and Luan Hoang and Saut, {Jean Claude}",
note = "Funding Information: The authors thank V.G. Bondarevsky and A.D. Bruno for valuable comments. CF acknowledges partial support by the NSF grant DMS-1516866. LH would like to thank the Departments of Mathematics at University of Tennessee (Knoxville), Indiana University (Bloomington), and Texas A&M University (College Station) for their hospitality during his visits in the Fall of 2017, when he partly worked on the manuscript of this paper. JCS acknowledges support by the French Science Foundation ANR, under grant GEODISP. Publisher Copyright: {\textcopyright} 2018, Wilmington Scientific Publisher. All rights reserved.",
year = "2018",
month = jun,
doi = "10.11948/2018.727",
language = "English",
volume = "8",
pages = "727--763",
journal = "Journal of Applied Analysis and Computation",
issn = "2156-907X",
number = "3",
}