A RANS 3D model with unbounded eddy viscosities

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1. [1] Adams R.A., Sobolev Spaces, Academic Press, 1975. Zbl0314.46030MR450957
2. [2] Batchelor G., The Theory of Homogeneous Turbulence, Cambridge University Press, 1953. Zbl0053.14404MR52268
3. [3] Bernardi C., Chacon-Rebello T., Lewandowski R., Murat F., A model for two coupled turbulent fluids, part 1: Analysis of the system, in: Series in Applied Mathematics, vol. 34, North-Holland, 2002, pp. 69-102. Zbl1034.35106
4. [4] Bernardi C., Chacon-Rebello T., Lewandowski R., Murat F., A model for two coupled turbulent fluids, part 2: Numerical approximation by spectral discretization, SIAM J. Numer. Anal.40 (2003) 2368-2394. Zbl1129.76327
5. [5] Bernardi C., Chacon-Rebello T., Lewandowski R., Murat F., A model for two coupled turbulent fluids, part 3: Approximation by finite elements, Numer. Math.98 (2004) 33-66. Zbl1129.76326MR2076053
6. [6] Blanke B., Delecluse P., Variability of the tropical atlantic ocean by a general circulation model with two different mixed layer physic, J. Phys. Ocean.23 (1993) 1363-1388. 
7. [7] Boccardo L., Gallouët T., Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal.87 (1989) 149-169. Zbl0707.35060MR1025884
8. [8] Brézis H., Analyse fonctionnelle, seconde ed., Masson, 1993. Zbl0511.46001MR697382
9. [9] Brossier F., Lewandowski R., On a first order closure system modelizing turbulent flows, Math. Modelling Numer. Anal.36 (2002) 345-372. Zbl1040.35057MR1906822
10. [10] Chacón Rebollo T., Oscillations due to the transport of microstructures, SIAM J. Appl. Math.48 (1988) 1128-1146. Zbl0656.76054MR960475
11. [11] Chen S., Foias C., Holm D., Olson E., Titi E.-S., Camassa–Holm equation as a closure model for turbulent channel and pipe flow, Phys. Rev. Lett.81 (1998) 5338-5341. Zbl1042.76525
12. [12] S. Clain, Analyse mathématique et numérique d'un modèle de chauffage par induction, PhD thesis, École Polytechnique Fédérale de Lausanne, 1994. 
13. [13] Clain S., Touzani R., Solution of a two-dimensional stationary induction heating problem without boundedness of the coefficients, RAIRO Model. Math. Anal. Numer.7 (1997) 845-870. Zbl0894.35035MR1489175
14. [14] Dauge M., Elliptic Boundary Value Problem on Corner Domains: Smoothness and Asymptotics 0, Springer-Verlag, 1988. Zbl0668.35001MR961439
15. [15] Deleersnijder E., A note on the stability functions of the Mellor–Yamada level 2 1/2 turbulence closure model, Bull. Soc. Roy. Sc. Liège61 (1992) 397-404. 
16. [16] DiPerna R.-J., Lions P.-L., Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math.98 (1989) 511-547. Zbl0696.34049MR1022305
17. [17] Erich J., Fedorovich E., Viegas D.X., Wyngaard J.C. (Eds.), Buoyant Convection in Geophysical Flows, Kluwer, 1998. Zbl0990.76501
18. [18] Gallouët T., Herbin R., Existence of a solution to a coupled elliptic system, Appl. Math. Lett.2 (1994) 49-55. Zbl0791.35043MR1350145
19. [19] Gallouët T., Lederer J., Lewandowski R., Murat F., Tartar L., On a turbulent system with unbounded eddy viscosities, J. Nonlinear Anal.52 (2003) 1051-1068. Zbl1013.35068MR1941245
20. [20] Girault V., Raviart P.-A., Finite Element Methods for Navier–Stokes Equations, Springer-Verlag, 1986. Zbl0585.65077
21. [21] Grisvard P., Elliptic Problems in Nonsmooth Domains, Pitman Advanced Publishing Program, Pitman, Boston, 1985. Zbl0695.35060MR775683
22. [22] Leray J., Schauder J., Topologie et équations fonctionnelles, Ann. Sci. École Norm. Sup.51 (1934) 45-78. Zbl60.0322.02MR1509338JFM60.0322.02
23. [23] Lewandowski R., Analyse Mathématique et Océanographie, Masson, 1997. 
24. [24] Lewandowski R., The mathematical analysis of the coupling of a turbulent kinetic energy equation to the Navier–Stokes equation with an eddy viscosity, Nonlinear Anal.28 (1997) 393-417. Zbl0863.35077
25. [25] Lewandowski R., Mohammadi B., Existence and positivity results for the θ–φ model and a modified k–ε model, Math. Models Methods Appl. Sci.3 (1993) 195-217. Zbl0773.76036
26. [26] R. Lewandowski, G. Pichot, Application of the fictive domain decomposition method and numerical simulations of water flow around a rigid net, 2006, submitted for publication. 
27. [27] P.-L. Lions, F. Murat, Renormalisation des équations elliptiques, 1995. 
28. [28] P.H. Maire, Etude d'une équation de diffusion non linéaire. Application à la discrétisation de l'équation de l'énergie cinétique turbulente pour un modèle de turbulence à une équation, Publications internes du CEA, 2001. 
29. [29] Mellor G.-L., Yamada T., Development of turbulence closure model for geophysical fluid problem, Rev. Geophys. Space Phys.20 (1982) 851-875. 
30. [30] Mohammadi B., Pironneau O., Analysis of the k-Epsilon Model, Masson, 1994. MR1296252
31. [31] Serrin J., Local behavior of solutions of quasi linear equations, Acta Math. (1964). Zbl0128.09101MR170096
32. [32] Spampacchia G., Équations elliptiques du second ordre à coefficients discontinus, Les presses de l'université de Montréal, 1966. Zbl0151.15501MR251373
33. [33] Temam R., Navier Stokes Equations, North-Holland, 1984. Zbl0568.35002MR769654

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