Asymptotic expansions in time for rotating incompressible viscous fluids
Accepted version
Peer-reviewed
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Repository DOI
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Authors
Hoang, LT
Titi, ES
Abstract
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 Poincar'e 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.
Description
Keywords
math.AP, math.AP, 35Q30, 76D05, 35C20, 76E07
Journal Title
Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Conference Name
Journal ISSN
0294-1449
1873-1430
1873-1430
Volume Title
38
Publisher
European Mathematical Society - EMS - Publishing House GmbH
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All rights reserved