Fluids with anisotropic viscosity

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1. [1] A. Babin, A. Mahalov and B. Nicolaenko, Global Splitting, Integrability and Regularity of 3D Euler and Navier Stokes Equations for Uniformly Rotating Fluids. Eur. J. Mech. 15 (1996) 291-300. Zbl0882.76096MR1400515
2. [2] J. M. Bony, Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires. Annales de l'École Normale Superieure 14 (1981) 209-246. Zbl0495.35024MR631751
3. [3] J.-Y. Chemin, Fluides parfaits incompressibles. Astérisque 230 (1995). Zbl0829.76003MR1340046
4. [4] J.-Y. Chemin, A propos d'un problème de pénalisation de type antisymétrique. J. Math. Pures. Appl. 76 (1997) 739-755. Zbl0896.35103MR1485418
5. [5] J.-Y. Chemin and N. Lerner, Flot de champs de vecteurs non Lipschitziens et équations de Navier-Stokes. J. Differential Equations 121 (1992) 314-328. Zbl0878.35089MR1354312
6. [6] J.-Y. Chemin and B. Desjardins, I. Gallagher and E. Grenier, Anisotropy and dispersion in rotating fluids, preprint of Universite d'Orsay (1999). Zbl0961.76085MR1735883
7. [7] B. Desjardins and E. Grenier, On the homogeneous model of wind driven ocean circulation. SIAM. J. Appl. Math. (to appear). Zbl0958.76092MR1740834
8. [8] B. Desjardins and E. Grenier, Dérivation of quasi-geostrophic potential vorticity equations. Adv. in Differential Equations 3 (1998), No. 5, 715-752. Zbl0967.76096MR1665870
9. [9] B. Desjardins and E. Grenier, Low Mach number limit of compressible flows in the whole space. Proceedmgs of the Royal Society of London A. 455 (1999) 2271-2279. Zbl0934.76080MR1702718
10. [10] H. Fujita and T. Kato, On the Navier Stokes initial value problem I. Archiv for Rational Mechanic Analysis 16 (1964) 269-315. Zbl0126.42301MR166499
11. [11] I. Gallagher, The Tridimensional Navier-Stokes Equations with Almost Bidimensional Data: Stability, Uniqueness and Life Span. International Mathematics Research Notices 18 (1997) 919-935. Zbl0893.35098MR1481611
12. [12] H. P. Greenspan, The theory of rotating fluids. Cambridge monographs on mechanics and applied mathematics (1969). Zbl0182.28103
13. [13] E. Grenier and N. Masmoudi, Ekman layers of rotating fluids, the case of well prepared initial data. Comm. Partial Differential Equations 22, No. 5-6, (1997) 953-975. Zbl0880.35093MR1452174
14. [14] D. Iftimie, La résolution des équations de Navier Stokes dans des domaines minces et la limite quasigéostrophique. Thèse de l'Université Paris 6 (1997). 
15. [15] D. Iftimie, The resolution of the Navier-Stokes equations in anisotropic spaces. Revista Matematica Ibero-Americana 15 (1999) 1-36. Zbl0923.35119MR1681635
16. [16] J. Leray, Essai sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math. 63 (1933) 193-248. Zbl59.0763.02JFM60.0726.05
17. [17] J. Pedlosky, Geophysical fluid dynamics, Springer (1979). Zbl0429.76001
18. [18] J. Rauch and M. Reed, Nonlinear microlocal analysis of semilinear hyperbolic systems in one space dimension. Duke Mathematical Journal 49 (1982) 397-475. Zbl0503.35055MR659948
19. [19] M. Sablé-Tougeron, Régularité microlocale pour des problèmes aux limites non linéaires. Annales de l'Institut Fourier 36 (1986) 39-82. Zbl0577.35004MR840713

1. Jean-Yves Chemin, Benoît Desjardins, Isabelle Gallagher, Emmanuel Grenier, Boundary layers and time oscillations in rotating fluids
2. Jean-Yves Chemin, Ping Zhang, The role of oscillations in the global wellposedness of the 3-D incompressible anisotropic Navier-Stokes equations