Attractor dimensions of three-dimensional Navier-Stokes- model for fast rotating fluids on generic-period domains: comparison with Navier-Stokes equations
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We study the fractal and Hausdor dimensions of the global attractor for the three-dimensional Navier-Stokes- model for fast ro- tating geophysical uids. The Navier-Stokes- model is a nonlinear dispersive regularization of the exact Navier-Stokes equations obtained by Lagrangian averaging and tend to the Navier-Stokes equations as ! 0+. We estimate upper bounds for the dimensions of the global attractor and study the dependence of the dimensions on the parameter . All the estimates are uniform in , and our estimates of attractor dimensions remain nite when ! 0+.
Abstract
We study the fractal and Hausdor dimensions of the global attractor for the three-dimensional Navier-Stokes- model for fast ro- tating geophysical uids. The Navier-Stokes- model is a nonlinear dispersive regularization of the exact Navier-Stokes equations obtained by Lagrangian averaging and tend to the Navier-Stokes equations as ! 0+. We estimate upper bounds for the dimensions of the global attractor and study the dependence of the dimensions on the parameter . All the estimates are uniform in , and our estimates of attractor dimensions remain nite when ! 0+.
참고문헌 (10)
- Babin, A., "Regularity and Integrability of 3D Euler and Navier-Stokes Equations for Rotating Fluids", J. Asympt. Anal., 15, pp.103~150 (1997)
- Babin, A., "Global Regularity of 3D Rotating Navier-Stokes Equations for Resonant Domains", Indiana Univ. Math. J., 48, pp.1133~1176 (1999)
- Jean-Yves Chemin, "Mathematical Geophysics: An introduction to rotating uids and the Navier-Stokes equations" (2006), Oxford University Press
- P. Constantin, "Determining modes and fractal dimension of turbulent ows", Journal of Fluid Mechanics, 150, pp.427~440 (1985)
- O. U. Velasco Fuentes, "Kelvin's discovery of Taylor columns", European Journal of Mechanics B, 2009, pp.28, 469~472
- J. D. Gibbon, "Length-scale estimates for the LANS-α equations in terms of the Reynolds number", Physica D, 220, pp.69~78 (2006)
- A. A. Ilyin, "Attractors for the Two-Dimensional Navier-Stokes-α Model:An α-Dependence study", Journal of Dynamics and Differential Equations, 15(4), pp.751~778 (2003)
- B. Kim, "Existence and continuity of exponential attractors of the three dimensional Navier-Stokes-α equations for uniformly rotating geophysical uids", Communications in Mathematical Sciences, 4(2), pp.399~452 (2006)
- Trahe, M., "Attractors for 3D Fast Rotating Navier-Stokes equations", Ph.D, pp.2002
- Robinson, J. C., "Infinite-Dimensional Dynamical Systems" (2001), Cambridge University Press