TY - JOUR
T1 - Asymptotic expansions in time for rotating incompressible viscous fluids
AU - Hoang, Luan T.
AU - Titi, Edriss S.
N1 - Publisher Copyright:
© 2020 Elsevier Masson SAS
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - Asymptotic expansions
KW - Long-time dynamics
KW - Navier-Stokes equations
KW - Rotating fluids
UR - http://www.scopus.com/inward/record.url?scp=85087177294&partnerID=8YFLogxK
U2 - 10.1016/j.anihpc.2020.06.005
DO - 10.1016/j.anihpc.2020.06.005
M3 - Article
AN - SCOPUS:85087177294
JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
SN - 0294-1449
ER -