JournalsaihpcVol. 38, No. 1pp. 109–137

Asymptotic expansions in time for rotating incompressible viscous fluids

  • Luan T. Hoang

    Department of Mathematics and Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409-1042, USA

  • Edriss S. Titi

    Department of Mathematics, 3368 TAMU, Texas A&M University, College Station, TX 77843-3368, USA, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK, Weizmann Institute of Science, Department of Computer Science and Applied Mathematics, P.O. Box 26, Rehovot, 76100, Israel
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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 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.

Cite this article

Luan T. Hoang, Edriss S. Titi, Asymptotic expansions in time for rotating incompressible viscous fluids. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 1, pp. 109–137

DOI 10.1016/J.ANIHPC.2020.06.005