Asymptotic expansions in time for rotating incompressible viscous fluids

Hoang, Luan T.; Titi, Edriss S.

doi:10.1016/j.anihpc.2020.06.005

Hoang, Luan T.¹ ; Titi, Edriss S.^2,^3,⁴

¹ a Department of Mathematics and Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409-1042, USA
² b Department of Mathematics, 3368 TAMU, Texas A&M University, College Station, TX 77843-3368, USA
³ c Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK
⁴ d Weizmann Institute of Science, Department of Computer Science and Applied Mathematics, P.O. Box 26, Rehovot, 76100, Israel

Annales de l'I.H.P. Analyse non linéaire, janvier – février 2021, Tome 38 (2021) no. 1, pp. 109-137.

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Résumé

We study the three-dimensional Navier–Stokes equations of rotating incompressible viscous fluids with periodic boundary conditions. The asymptotic expansions, as time goes to infinity, are derived in all Gevrey spaces for any Leray–Hopf weak solutions in terms of oscillating, exponentially decaying functions. The results are established for all non-zero rotation speeds, and for both cases with and without the zero spatial average of the solutions. Our method makes use of the Poincaré waves to rewrite the equations, and then implements the Gevrey norm techniques to deal with the resulting time-dependent bi-linear form. Special solutions are also found which form infinite dimensional invariant linear manifolds.

Reçu le : 2019-10-21
Révisé le : 2020-04-15
Accepté le : 2020-06-10

DOI : 10.1016/j.anihpc.2020.06.005

Classification : 35Q30, 76D05, 35C20, 76E07
Mots-clés : Navier-Stokes equations, Rotating fluids, Asymptotic expansions, Long-time dynamics

Affiliations des auteurs :

Hoang, Luan T. ¹ ; Titi, Edriss S. ^{2, 3, 4}

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     title = {Asymptotic expansions in time for rotating incompressible viscous fluids},
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Hoang, Luan T.; Titi, Edriss S. Asymptotic expansions in time for rotating incompressible viscous fluids. Annales de l'I.H.P. Analyse non linéaire, janvier – février 2021, Tome 38 (2021) no. 1, pp. 109-137. doi : 10.1016/j.anihpc.2020.06.005. http://www.numdam.org/articles/10.1016/j.anihpc.2020.06.005/

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