Asymptotic Expansions in Time for Rotating Incompressible Viscous Fluids
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Asymptotic Expansions in Time for Rotating Incompressible Viscous Fluids

  • Author(s): Hoang, Luan T
  • Titi, Edriss S
  • et al.
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.

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