Limiting behavior for an iterated viscosity

Ciprian Foias; Michael S. Jolly; Oscar P. Manley

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2000)

  • Volume: 34, Issue: 2, page 353-376
  • ISSN: 0764-583X

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Foias, Ciprian, Jolly, Michael S., and Manley, Oscar P.. "Limiting behavior for an iterated viscosity." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 34.2 (2000): 353-376. <http://eudml.org/doc/193990>.

@article{Foias2000,
author = {Foias, Ciprian, Jolly, Michael S., Manley, Oscar P.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {ordinary differential equation; low wave number velocity mode; iterative process; two-dimensional Navier-Stokes equations; kinematic viscosity; iterated viscosity; limiting dynamical system},
language = {eng},
number = {2},
pages = {353-376},
publisher = {Dunod},
title = {Limiting behavior for an iterated viscosity},
url = {http://eudml.org/doc/193990},
volume = {34},
year = {2000},
}

TY - JOUR
AU - Foias, Ciprian
AU - Jolly, Michael S.
AU - Manley, Oscar P.
TI - Limiting behavior for an iterated viscosity
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2000
PB - Dunod
VL - 34
IS - 2
SP - 353
EP - 376
LA - eng
KW - ordinary differential equation; low wave number velocity mode; iterative process; two-dimensional Navier-Stokes equations; kinematic viscosity; iterated viscosity; limiting dynamical system
UR - http://eudml.org/doc/193990
ER -

References

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  1. [1] P. Constantin and C. Foias, Navier-Stokes Equations, Univ. Chicago Press, Chicago, IL (1988). Zbl0687.35071MR972259
  2. [2] N. Dunford and J. T. Schwartz, Book Linear Operators, Wiley, New York (1958) Part II. Zbl0084.10402
  3. [3] C. Foias, What do the Navier-Stokes equations tell us about turbulence? in Harmonic analysis and nonlinear differential equations (Riverside, CA, 1995). Contemp. Math. 208 (1997) 151-180. Zbl0890.76030MR1467006
  4. [4] C. Foias, O. P. Manley and R. Temam, Modelling of the interaction of small and large eddies in two-dimensional turbulent flows. RAIRO Modél. Math. Anal. Numér. 22 (1988) 93-118. Zbl0663.76054MR934703
  5. [5] C. Foias, O. P. Manley and R. Temam, Approximate inertial manifolds and effective viscosity in turbulent flows. Phys. Fluids A 3 (1991) 898-911. Zbl0732.76001MR1205478
  6. [6] C. Foias, O. P. Manley and R. Temam, Iterated approximate inertial manifolds for Navier-Stokes equations in 2-D. J. Math. Anal. Appl. 178 (1994) 567-583. Zbl0806.76015MR1238896
  7. [7] C. Foias, O. P. Manley, R. Temam and Y. M. Treve, Asymptotic analysis of the Navier-Stokes equations. Phys. D 9 (1983) 157-188. Zbl0584.35007MR732571
  8. [8] C. Foias and B. Nicolaenko, On the algebra of the curl operator in the Navier-Stokes equations (in preparation). 
  9. [9] R. H. Kraichnan, Inertial ranges in two-dimensional turbulence. Phys. Fluids 10 (1967) 417-1423. 
  10. [10] W. Heisenberg, On the theory of statistical and isotropic turbulence. Proc. Roy.Soc. Lond. Ser. A. 195 (1948) 402-406. Zbl0035.25605MR30851
  11. [11] E. Hopf, A mathematical example displaying features of turbulence. Comm. Appl. Math. 1 (1948) 303-322. Zbl0031.32901MR30113
  12. [12] R. Temam, Infinite-dimensional Dynamical Systems in Mechanics and Physics, 2nd édition, Springer-Verlag, New York (1997). Zbl0871.35001MR1441312
  13. [13] T. von Karman, Tooling up mathematics for engineering. Quarterly Appl. Math. 1 (1943) 2-6. 

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