TY - JOUR
T1 - Asymptotic expansions in time for rotating incompressible viscous fluids
AU - Hoang, Luan T.
AU - Titi, Edriss S.
N1 - Funding Information:
The work of E.S.T. was supported in part by the Einstein Stiftung/Foundation - Berlin, through the Einstein Visiting Fellow Program, and by the John Simon Guggenheim Memorial Foundation . The authors would like to thank Ciprian Foias for his insights, inspiring and stimulating discussions.
Publisher Copyright:
© 2020 L'Association Publications de l'Institut Henri Poincaré
PY - 2021/1/1
Y1 - 2021/1/1
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
SN - 0294-1449
VL - 38
SP - 109
EP - 137
JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
IS - 1
ER -