Limiting behavior for an iterated viscosity
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 34 (2000) no. 2, p. 353-376
@article{M2AN_2000__34_2_353_0,
     author = {Foia\c s, Ciprian and Jolly, Michael S. and Manley, Oscar P.},
     title = {Limiting behavior for an iterated viscosity},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {34},
     number = {2},
     year = {2000},
     pages = {353-376},
     zbl = {0962.76022},
     mrnumber = {1765664},
     language = {en},
     url = {http://http://www.numdam.org/item/M2AN_2000__34_2_353_0}
}
Foias, Ciprian; Jolly, Michael S.; Manley, Oscar P. Limiting behavior for an iterated viscosity. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 34 (2000) no. 2, pp. 353-376. http://www.numdam.org/item/M2AN_2000__34_2_353_0/

[1] P. Constantin and C. Foias, Navier-Stokes Equations, Univ. Chicago Press, Chicago, IL (1988). | MR 972259 | Zbl 0687.35071

[2] N. Dunford and J. T. Schwartz, Book Linear Operators, Wiley, New York (1958) Part II. | Zbl 0084.10402

[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. | MR 1467006 | Zbl 0890.76030

[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. | Numdam | MR 934703 | Zbl 0663.76054

[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. | MR 1205478 | Zbl 0732.76001

[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. | MR 1238896 | Zbl 0806.76015

[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. | MR 732571 | Zbl 0584.35007

[8] C. Foias and B. Nicolaenko, On the algebra of the curl operator in the Navier-Stokes equations (in preparation).

[9] R. H. Kraichnan, Inertial ranges in two-dimensional turbulence. Phys. Fluids 10 (1967) 417-1423.

[10] W. Heisenberg, On the theory of statistical and isotropic turbulence. Proc. Roy.Soc. Lond. Ser. A. 195 (1948) 402-406. | MR 30851 | Zbl 0035.25605

[11] E. Hopf, A mathematical example displaying features of turbulence. Comm. Appl. Math. 1 (1948) 303-322. | MR 30113 | Zbl 0031.32901

[12] R. Temam, Infinite-dimensional Dynamical Systems in Mechanics and Physics, 2nd édition, Springer-Verlag, New York (1997). | MR 1441312 | Zbl 0871.35001

[13] T. Von Karman, Tooling up mathematics for engineering. Quarterly Appl. Math. 1 (1943) 2-6.