Fast singular oscillating limits and global regularity for the 3D primitive equations of geophysics
Anatoli Babin; Alex Mahalov; Basil Nicolaenko
- Volume: 34, Issue: 2, page 201-222
- ISSN: 0764-583X
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topBabin, Anatoli, Mahalov, Alex, and Nicolaenko, Basil. "Fast singular oscillating limits and global regularity for the 3D primitive equations of geophysics." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 34.2 (2000): 201-222. <http://eudml.org/doc/193983>.
@article{Babin2000,
author = {Babin, Anatoli, Mahalov, Alex, Nicolaenko, Basil},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {three-dimensional primitive equations; primitive Navier-Stokes equations; infinite time regularity; fast singular oscillating limits; geophysical flows; infinite time intervals; regular solutions; strong stratification; global existence; Littlewood-Paley dyadic decomposition; limit resonance equations; convergence},
language = {eng},
number = {2},
pages = {201-222},
publisher = {Dunod},
title = {Fast singular oscillating limits and global regularity for the 3D primitive equations of geophysics},
url = {http://eudml.org/doc/193983},
volume = {34},
year = {2000},
}
TY - JOUR
AU - Babin, Anatoli
AU - Mahalov, Alex
AU - Nicolaenko, Basil
TI - Fast singular oscillating limits and global regularity for the 3D primitive equations of geophysics
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2000
PB - Dunod
VL - 34
IS - 2
SP - 201
EP - 222
LA - eng
KW - three-dimensional primitive equations; primitive Navier-Stokes equations; infinite time regularity; fast singular oscillating limits; geophysical flows; infinite time intervals; regular solutions; strong stratification; global existence; Littlewood-Paley dyadic decomposition; limit resonance equations; convergence
UR - http://eudml.org/doc/193983
ER -
References
top- [1] V. I. Arnold, Small denominators. I. Mappings of the circumference onto itself. Amer. Math. Soc. Transl. Ser. 2 46 (1965)213-284. Zbl0152.41905
- [2] V. I. Arnold and B. A. Khesin, Topological Methods in Hydrodynamics. Appl. Math. Sci. 125 (1997). Zbl0902.76001MR1612569
- [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. Zbl1022.76010MR1690099
- [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. Zbl0872.76097MR1685858
- [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. Zbl0882.76096MR1400515
- [6] A. Babin, A. Mahalov and B. Nicolaenko, Resonances and regularîty for Boussinesq equations. Russian J. Math. Phys. 4, No. 4, (1996) 417-428. Zbl0955.76521MR1470444
- [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. Zbl0883.76014MR1444000
- [8] A. Babin, A. Mahalov and B. Nicolaenko, Global regularity and ïntegrability of 3D Euler and Navier-Stokes equations for uniformly rotating fluids. Asympt. Anal. 15 (1997) 103-150. Zbl0890.35109MR1480996
- [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. Zbl0889.76007MR1472094
- [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. Zbl0957.76092
- [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. Zbl0912.76092
- [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. Zbl1035.76055MR1710277
- [13] A. Babin, A. Mahalov and B. Nicolaenko, Global regularity of 3D rotating Navier-Stokes equations for resonant domains. Lett. Appl. Math. (to appear). Zbl0932.35160MR1752139
- [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. Zbl0932.35160MR1736966
- [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).
- [16] A. V. Babin and M. I. Vishik, Attractors of Evolution Equations, North-Holland, Amsterdam (1992). Zbl0778.58002MR1156492
- [17] C. Bardos and S. Benachour, Domaine d'analycité des solutions de l'équation d'Euler dans un ouvert de Rn. Annali della Scuola Normale Superiore di Pisa 4 (1977) 647-687. Zbl0366.35022MR454413
- [18] P. Bartello, Geostrophic adjustment and inverse cascades in rotating stratified turbulence. J. Atm. Sci. 52, No. 24, (1995)4410-4428. MR1370126
- [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. Zbl0811.35097MR1278890
- [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. Zbl0509.35067MR673830
- [21] J.-Y. Chemin, A propos d'un problème de pénalisation de type antisymétrique. Proc. Parts Acad. Sci. 321 (1995) 861-864. Zbl0842.35082MR1355842
- [22] P. Constantin, The Littlewood-Paley spectrum in two-dimensional turbulence, Theor. and Comp. Fluid Dyn. 9, No. 3/4, (1997) 183-191. Zbl0907.76042
- [23] P. Constantin and C. Foias, Navier-Stokes Equations, The University of Chicago Press (1988). Zbl0687.35071MR972259
- [24] A. Craya, Contribution à l'analyse de la turbulence associée à des vitesses moyennes. P.S.T. Ministère de l'Air 345 (1958). Zbl0077.39605MR98536
- [25] P. G. Drazin and W. H. Reid, Hydrodynamic Stability, Cambridge University Press (1981). Zbl0449.76027MR604359
- [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. Zbl0849.35106MR1387463
- [27] I. Gallagher, Un résultat de stabilité pour les équations des fluides tournants, C.R. Acad. Sci. Paris, Série I (1997) 183-186. Zbl0878.76081MR1438380
- [28] I. Gallagher, Asymptotics of the solutions of hyperbolic equations with a skew-symmetrie perturbation. J. Differential Equations 150 (1998) 363-384. Zbl0921.35095MR1658597
- [29] I. Gallagher, Applications of Schochet's methods to parabolic equations. J. Math. Pures Appl. 77 (1998) 989-1054. Zbl1101.35330MR1661025
- [30] E. Grenier, Rotating fluids and inertial waves. Proc. Acad. Sci. Paris Ser. 1 321 (1995) 711-714. Zbl0843.35073MR1354711
- [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. Zbl0815.35066MR1219817
- [32] J. L. Joly, G. Métivier and J. Rauch, Resonant one-dimensional nonlinear geometric optics. J. Funct. Anal. 114 (1993) 106-231. Zbl0851.35023MR1220985
- [33] J. L. Joly, G. Métivier and J. Rauch, Coherent nonlinear waves and the Wiener algebra. Ann. Inst. Fourier 44 (1994) 167-196. Zbl0791.35019MR1262884
- [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. Zbl0836.35087MR1305424
- [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. Zbl0961.76071
- [36] O. A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, 2nd édition, Gordon and Breach, New York (1969). Zbl0184.52603MR254401
- [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. Zbl0846.35106MR1350974
- [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. Zbl0992.86001MR1454171
- [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. Zbl0708.76044MR1076072
- [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.
- [41] O. Métais and J. R. Herring, Numerical experiments of freely evolving turbulence in stably stratified fluids. J. Fluid Mech. 202 (1989) 117.
- [42] J. Pedlosky, Geophysical Fluid Dynamics, 2nd édition, Springer-Verlag (1987). Zbl0713.76005
- [43] H. Poincaré, Sur la précession des corps déformables. Bull. Astronomique 27 (1910) 321.
- [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. Zbl0787.34039MR1179539
- [45] S. Schochet, Fast singular limits of hyperbolic PDE's. J. Differential Equations 114 (1994) 476-512. Zbl0838.35071MR1303036
- [46] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton University Press (1970). Zbl0207.13501MR290095
- [47] S. L. Sobolev, Ob odnoi novoi zadache matematicheskoi fiziki. Izvestiia Akademii Nauk SSSR, Ser. Matematicheskaia 18, No. 1, (1954) 3-50.
- [48] R. Temam, Navier-Stokes Equations: Theory and Numerical Analysis, North-Holland, Amsterdam (1984). Zbl0568.35002MR769654
- [49] R. Temam, Navier-Stokes Equations and Nonlinear Functional Analysis, SIAM, Philadelphia (1983). Zbl0833.35110MR764933
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