On the regularity of three-dimensional rotating euler-boussinesq equations

Mathematical Models and Methods in Applied Sciences

Volumn 9, Issue 7, 1999, Pages 1089-1121

  Babin, A ^a,b   Mahalov, A ^c   Nicolaenko, B ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b RUSSIAN UNIVERSITY OF TRANSPORT   (Russian Federation)

^c ARIZONA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033430020     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021820259900049X     Document Type: Article

References (31)

1. V. I. Arnold, Small denominators. I. Mappings of the circumference onto itself, Amer. Math. Soc. Transl. Ser. 2 46 (1965) 213-284.
2. V. I. Arnold and B. A. Khesin, Topological Methods in Hydrodynamics, Applied Mathematical Sciences, Vol. 125 (Springer-Verlag, 1997).
3. 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, eds. K. Kirchgässner and A. Mielke (World Scientific, 1995), pp. 145-157.
4. A. Babin, A. Mahalov and B. Nicolaenko, Global splitting, integrability and regularity of 3-D Euler and Navier-Stokes equations for uniformly rotating fluids, Euro. J. Mech., B/Fluids 15 (1996) 291-300.
5. A. Babin, A. Mahalov and B. Nicolaenko, Resonances and regularity for Boussinesq equations, Russian J. Math. Phys. 4 (1996) 417-428.
6. A. Babin, A. Mahalov and B. Nicolaenko, Regularity and integrability of rotating shallow-water equations, Proc. Acad. Sci. Paris 324 (1997) 593-598.
7. A. Babin, A. Mahalov and B. Nicolaenko, Global regularity and integrability of 3-D Euler and Navier-Stokes equations for uniformly rotating fluids, Asymptotic Anal. 15 (1997) 103-150.
8. A. Babin, A. Mahalov and B. Nicolaenko, Global splitting and regularity of rotating shallow-water equations, Euro. J. Mech., B/Fluids 16 (1997) 725-754.
9. A. Babin, A. Mahalov and B. Nicolaenko, On the nonlinear baroclinic waves and adjustment of pancake dynamics, Theor. Comput. Fluid Dynamics 11 (1998) 215-235.
10. A. Babin, A. Mahalov, B. Nicolaenko and Y. Zhou, On the asymptotic regimes and the strongly stratified limit of rotating Boussinesq equations, Theor. Comput. Fluid Dynamics 9 (1997) 223-251.
11. P. Bartello, Geostrophic adjustment and inverse cascades in rotating stratified turbulence, J. Atm. Sci. 52 (1995) 4410-4428.
12. 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 (1994) 1023-1068.
13. J.-Y. Chemin, A propos d'un probleme de pénalisation de type antisymétrique, Proc. Paris Acad. Sci. 321 (1995) 861-864.
14. M. J. P. Cullen, New mathematical developments in atmosphere and ocean dynamics and their application to computer simulations, UK Met Office, Forecasting Research Division, Report No. 48 (1998).
15. P. F. Embid and A. J. Majda, Averaging over fast gravity waves for geophysical flows with arbitrary potential vorticity, Comm. Partial Differential Equations 21 (1996) 619-658.
16. H. J. S. Fernando and J. C. R. Hunt, Some aspects of turbulence and mixing in stably stratified layers, Dynamics Atm. Oceans 23 (1996) 35.
17. I. Gallagher, Un résultat de stabilité pour les équations des fluides tournants, C. R. Acad. Sci. Paris, Série I (1997) 183-186.
18. I. Gallagher, Asymptotics of the solutions of hyperbolic equations with a skewsymmetric perturbation, preprint, University of Paris-6 (1997).
19. I. Gallagher, Applications of Schochet's methods to parabolic equations, preprint, University of Paris-6 (1998).
20. E. Grenier, Rotating fluids and inertial waves, Proc. Acad Sci. Paris, t. 321, Ser. 1 (1995) 711-714 (see also Ph.D. thesis preprint, University of Paris-6).
21. 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. See more references in bibliography of Ref. 7.
22. J. L. Lions, R. Temam and S. Wang, Geostrophic asymptotics of the primitive equations of the atmosphere, Topological Methods Nonlinear Anal. 4 (1994) 253-287, special issue dedicated to J. Leray.
23. A. Mahalov and P. S. Marcus, Long-time averaged rotating shallow-water equations, Proc. the First Asian Computational Fluid Dynamics Conference, eds. W. H. Hui, Y.-K. Kwok and J. R. Chasnov (Hong Kong University of Science and Technology, 1995), Vol. 3, pp. 1227-1230.
24. A. Mahalov and Y. Zhou, Analytical and phenomenological studies of rotating turbulence, Phys. Fluids 8 (1996) 2138-2152.
25. J. C. McWilliams, A note on a uniformly valid model spanning the regimes of geostrophic and isotropic stratified turbulence: balanced turbulence, J. Atm. Sci. 42 (1985) 1773-1774.
26. O. Métais and J. R. Herring, Numerical experiments of freely evolving turbulence in stably stratified fluids, J. Fluid Mech. 202 (1989) 117.
27. J. Pedlosky, Geophysical Fluid Dynamics (Springer-Verlag, 1987), 2nd edition.
28. H. Poincaré, Sur la précession des corps déformables, Bull. Astron. 27 (1910) 321.
29. J. J. Riley, R. W. Metcalfe and M. A. Weisman, Direct numerical simulations of homogeneous turbulence in density-stratified fluids, Proc. AIP Conf. Nonl. Prop. of Internal Waves, ed. B. J. West (AIP, 1981), p. 79.
30. S. Schochet, Fast singular limits of hyperbolic PDE's, J. Differential Equations 114 (1994) 476-512.
31. S. L. Sobolev, Ob odnoi novoi zadache matematicheskoi fiziki, Izv. Akad. Nauk SSSR, Ser. Mat. 18 (1954) 3-50.