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ROTATING NAVIER-STOKES-α EQUATIONS: EXPONENTIAL ATTRACTORS IN HILBERT AND BANACH SPACES

Bong-Sik Kim
장전수학회 (Jangjeon Mathematical Society)|2022.01|Advanced Studies in Contemporary Mathematics|제32권 제1호|pp. 31-44

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키워드

Exponential AttractorsGlobal AttractorsNavier-Stokes Equations
주제분류수학

초록

This article covers the construction of exponential attrac- tors in two different functional space settings; one is in Hilbert's space, and the other is in the Banach space. The former relies on the squeezing properties of solution trajectories, but the latter does not. We present these different methods for constructing exponential attractors using the three-dimensional rotating Navier-Stokes-α equations.

Abstract

This article covers the construction of exponential attrac- tors in two different functional space settings; one is in Hilbert's space, and the other is in the Banach space. The former relies on the squeezing properties of solution trajectories, but the latter does not. We present these different methods for constructing exponential attractors using the three-dimensional rotating Navier-Stokes-α equations.

참고문헌 (13)

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  2. A. Babin, "Global Regularity of 3D Rotating Navier-Stokes Equations for Resonant Domains", Indiana Univ. Math. J., 48, pp.1133~1176 (1999)
  3. Le Dung, B. Nicolaenko, "Exponential attractors in Banach spaces", J. Dynamics and Differential Equations, 13(4), pp.791~806 (2001)
  4. A. Eden, "Exponential Attractors for Evolution Equations" (1994), Wiley and Masson
  5. Hale, J. K., "Asymptotic Behavior of Dissipative Systems", AMS, ~ (1988)
  6. D. D. Holm, "Euler-Poincare Models of Ideal Fluids with Nonlinear Dispersion", Phys. Rev. Lett, 80, pp.4173~4176 (1998)
  7. J. D. Gibbon, "Length-scale estimates for the LANS-α equations in terms of the Reynolds number", Physica D, 220, pp.69~78 (2006)
  8. A. A. Ilyin, "Attractors for the Two-Dimensional Navier-Stokes-α Model:An α-Dependence study", Journal of Dynamics and Di erential Equations, 15(4), pp.751~778 (2003)
  9. B. Kim, "Existence and continuity of exponential attractors of the three dimensional Navier-Stokes-α equations for uniformly rotating geophysical uids", Comm. Math. Sci, 4(2), pp.399~452 (2006)
  10. 김봉식, "Attractor dimensions of three-dimensional Navier-Stokes- model for fast rotating fluids on generic-period domains: comparison with Navier-Stokes equations", Advanced Studies in Contemporary Mathematics, 29(1), pp.39~58 (2019), 장전수학회[DOI]
  11. Vittorino Pata, "Two Questions Arising in the Theory of Attractors", Evolution Equa-tions and Control Theory, 8(3), pp.663~668 (2019)
  12. Roger Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics" (1997), Springer
  13. M. Trahe, "Attractors for 3D Fast Rotating Navier-Stokes equations", Ph.D, pp.2002

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