Free Access
Issue
ESAIM: M2AN
Volume 34, Number 2, March/April 2000
Special issue for R. Teman's 60th birthday
Page(s) 201 - 222
DOI https://doi.org/10.1051/m2an:2000138
Published online 15 April 2002
  1. V.I. Arnold, Small denominators. I. Mappings of the circumference onto itself. Amer. Math. Soc. Transl. Ser. 2. 46 (1965) 213-284. [Google Scholar]
  2. V.I. Arnold and B.A. Khesin, Topological Methods in Hydrodynamics. Appl. Math. Sci. 125 (1997). [Google Scholar]
  3. J. Avrin, A. Babin, A. Mahalov and B. Nicolaenko, On regularity of solutions of 3D Navier-Stokes equations. Appl. Anal. 71 (1999) 197-214. [CrossRef] [MathSciNet] [Google Scholar]
  4. A. Babin, A. Mahalov and B. Nicolaenko, Long-time averaged Euler and Navier-Stokes equations for rotating fluids, In Structure and Dynamics of Nonlinear Waves in Fluids, 1994 IUTAM Conference, K. Kirchgässner and A. Mielke Eds, World Scientific (1995) 145-157. [Google Scholar]
  5. A. Babin, A. Mahalov and B. Nicolaenko, Global splitting, integrability and regularity of 3D Euler and Navier-Stokes equations for uniformly rotating fluids. Europ. J. Mech. B/Fluids 15, No. 3, (1996) 291-300. [Google Scholar]
  6. A. Babin, A. Mahalov and B. Nicolaenko, Resonances and regularity for Boussinesq equations. Russian J. Math. Phys. 4, No. 4, (1996) 417-428. [Google Scholar]
  7. A. Babin, A. Mahalov and B. Nicolaenko, Regularity and integrability of rotating shallow-water equations. Proc. Acad. Sci. Paris Ser. 1 324 (1997) 593-598. [Google Scholar]
  8. A. Babin, A. Mahalov and B. Nicolaenko, Global regularity and integrability of 3D Euler and Navier-Stokes equations for uniformly rotating fluids. Asympt. Anal. 15 (1997) 103-150. [Google Scholar]
  9. A. Babin, A. Mahalov and B. Nicolaenko, Global splitting and regularity of rotating shallow-water equations. Eur. J. Mech., B/Fluids 16, No. 1, (1997) 725-754. [Google Scholar]
  10. A. Babin, A. Mahalov and B. Nicolaenko, On the nonlinear baroclinic waves and adjustment of pancake dynamics. Theor. and Comp. Fluid Dynamics 11 (1998) 215-235. [CrossRef] [Google Scholar]
  11. A. Babin, A. Mahalov, B. Nicolaenko and Y. Zhou, On the asymptotic regimes and the strongly stratified limit of rotating Boussinesq equations. Theor. and Comp. Fluid Dyn. 9 (1997) 223-251. [CrossRef] [Google Scholar]
  12. A. Babin, A. Mahalov and B. Nicolaenko, On the regularity of three-dimensional rotating Euler-Boussinesq equations. Math. Models Methods Appl. Sci., 9, No. 7 (1999) 1089-1121. [Google Scholar]
  13. A. Babin, A. Mahalov and B. Nicolaenko, Global regularity of 3D rotating Navier-Stokes equations for resonant domains. Lett. Appl. Math. (to appear). [Google Scholar]
  14. A. Babin, A. Mahalov and B. Nicolaenko, Global Regularity of 3D Rotating Navier-Stokes Equations for Resonant Domains. Indiana University Mathematics Journal 48, No. 3, (1999) 1133-1176. [Google Scholar]
  15. A. Babin, A. Mahalov and B. Nicolaenko, Fast singular oscillating limits of stably stratified three-dimensional Euler-Boussinesq equations and ageostrophic wave fronts, to appear in Mathematics of Atmosphere and Ocean Dynamics, Cambridge University Press (1999). [Google Scholar]
  16. A.V. Babin and M.I. Vishik, Attractors of Evolution Equations, North-Holland, Amsterdam (1992). [Google Scholar]
  17. C. Bardos and S. Benachour, Domaine d'analycité des solutions de l'équation d'Euler dans un ouvert de Formula . Annali della Scuola Normale Superiore di Pisa 4 (1977) 647-687. [Google Scholar]
  18. P. Bartello, Geostrophic adjustment and inverse cascades in rotating stratified turbulence. J. Atm. Sci. 52, No. 24, (1995) 4410-4428. [Google Scholar]
  19. A.J. Bourgeois and J.T. Beale, Validity of the quasigeostrophic model for large-scale flow in the atmosphere and the ocean, SIAM J. Math. Anal. 25, No. 4, (1994) 1023-1068. [Google Scholar]
  20. L. Caffarelli, R. Kohn and L. Nirenberg, Partial regularity of suitable weak solutions of the Navier-Stokes equations. Comm. Pure Appl. Math. 35 (1982) 771-831. [CrossRef] [MathSciNet] [Google Scholar]
  21. J.-Y. Chemin, A propos d'un probleme de pénalisation de type antisymétrique. Proc. Paris Acad. Sci. 321 (1995) 861-864. [Google Scholar]
  22. P. Constantin, The Littlewood-Paley spectrum in two-dimensional turbulence, Theor. and Comp. Fluid Dyn. 9, No. 3/4, (1997) 183-191. [Google Scholar]
  23. P. Constantin and C. Foias, Navier-Stokes Equations, The University of Chicago Press (1988). [Google Scholar]
  24. A. Craya, Contribution à l'analyse de la turbulence associée à des vitesses moyennes. P.S.T. Ministère de l'Air 345 (1958). [Google Scholar]
  25. P.G. Drazin and W.H. Reid, Hydrodynamic Stability, Cambridge University Press (1981). [Google Scholar]
  26. P.F. Embid and A.J. Majda, Averaging over fast gravity waves for geophysical flows with arbitrary potential vorticity, Comm. Partial Diff. Eqs. 21 (1996) 619-658. [Google Scholar]
  27. I. Gallagher, Un résultat de stabilité pour les équations des fluides tournants, C.R. Acad. Sci. Paris, Série I (1997) 183-186. [Google Scholar]
  28. I. Gallagher, Asymptotics of the solutions of hyperbolic equations with a skew-symmetric perturbation. J. Differential Equations 150 (1998) 363-384. [Google Scholar]
  29. I. Gallagher, Applications of Schochet's methods to parabolic equations. J. Math. Pures Appl. 77 (1998) 989-1054. [Google Scholar]
  30. E. Grenier, Rotating fluids and inertial waves. Proc. Acad Sci. Paris Ser. 1 321 (1995) 711-714. [Google Scholar]
  31. J.L. Joly, G. Métivier and J. Rauch, Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves. Duke Math. J. 70 (1993) 373-404. [CrossRef] [MathSciNet] [Google Scholar]
  32. J.L. Joly, G. Métivier and J. Rauch, Resonant one-dimensional nonlinear geometric optics. J. Funct. Anal. 114 (1993) 106-231. [CrossRef] [MathSciNet] [Google Scholar]
  33. J.L. Joly, G. Métivier and J. Rauch, Coherent nonlinear waves and the Wiener algebra. Ann. Inst. Fourier 44 (1994) 167-196. [Google Scholar]
  34. J.L. Joly, G. Métivier and J. Rauch, Coherent and focusing multidimensional nonlinear geometric optics. Ann. Scient. E. N. S. Paris 4 (1995) 28, 51-113. [Google Scholar]
  35. D.A. Jones, A. Mahalov and B. Nicolaenko, A numerical study of an operator splitting method for rotating flows with large ageostrophic initial data. Theor. and Comp. Fluid Dyn. 13, No. 2, (1998) 143-159. [Google Scholar]
  36. O.A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, 2nd edition, Gordon and Breach, New York (1969). [Google Scholar]
  37. J.-L. Lions, R. Temam and S. Wang, Geostrophic asymptotics of the primitive equations of the atmosphere. Topological Methods in Nonlinear Analysis 4 (1994) 253-287, special issue dedicated to J. Leray. [Google Scholar]
  38. J.-L. Lions, R. Temam and S. Wang, A simple global model for the general circulation of the atmosphere. Comm. Pure Appl. Math. 50 (1997) 707-752. [CrossRef] [MathSciNet] [Google Scholar]
  39. A. Mahalov, S. Leibovich and E.S. Titi, Invariant helical subspaces for the Navier-Stokes Equations. Arch. for Rational Mech. and Anal. 112, No. 3, (1990) 193-222. [Google Scholar]
  40. A. Mahalov and P.S. Marcus, Long-time averaged rotating shallow-water equations, Proc. of the First Asian Computational Fluid Dynamics Conference, W.H. Hui, Y.-K. Kwok and J.R. Chasnov Eds, vol. 3, Hong Kong University of Science and Technology (1995) 1227-1230. [Google Scholar]
  41. O. Métais and J.R. Herring, Numerical experiments of freely evolving turbulence in stably stratified fluids. J. Fluid Mech. 202 (1989) 117. [CrossRef] [Google Scholar]
  42. J. Pedlosky, Geophysical Fluid Dynamics, 2nd edition, Springer-Verlag (1987). [Google Scholar]
  43. H. Poincaré, Sur la précession des corps déformables. Bull. Astronomique 27 (1910) 321. [Google Scholar]
  44. G. Raugel and G. Sell, Navier-Stokes equations on thin 3D domains. I. Global attractors and global regularity of solutions, J. Amer. Math. Soc. 6, No. 3, (1993) 503-568. [Google Scholar]
  45. S. Schochet, Fast singular limits of hyperbolic PDE's. J. Differential Equations 114 (1994) 476-512. [Google Scholar]
  46. E.M. Stein, Singular integrals and differentiability properties of functions, Princeton University Press (1970). [Google Scholar]
  47. S.L. Sobolev, Ob odnoi novoi zadache matematicheskoi fiziki. Izvestiia Akademii Nauk SSSR, Ser. Matematicheskaia. 18, No. 1, (1954) 3-50. [Google Scholar]
  48. R. Temam, Navier-Stokes Equations: Theory and Numerical Analysis, North-Holland, Amsterdam (1984). [Google Scholar]
  49. R. Temam, Navier-Stokes Equations and Nonlinear Functional Analysis, SIAM, Philadelphia (1983). [Google Scholar]

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