Chapter 5 On the influence of the Earth's rotation on geophysical flows

Handbook of Mathematical Fluid Dynamics

Volumn 4, Issue , 2007, Pages 201-329

  Gallagher, Isabelle ^a   Saint Raymond, Laure ^b  

^a INSTITUT DE MATHÉMATIQUES DE JUSSIEU   (France)

^b UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 59649116493     PISSN: 18745792     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1874-5792(07)80009-7     Document Type: Chapter

References (57)

1. T. Alazard, Low Mach number limit of the full Navier-Stokes equations, Archive for Rational Mechanics and Analysis, to appear.
2. Babin A., Mahalov A., and Nicolaenko B. Global splitting, integrability and regularity of 3D Euler and Navier-Stokes equations for uniformly rotating fluids. European Journal of Mechanics 15 (1996) 291-300
3. Babin A., Mahalov A., and Nicolaenko B. Resonances and regularity for Boussinesq equations. Russian Journal of Mathematical Physics 4 (1996) 417-428
4. Babin A., Mahalov A., and Nicolaenko B. Global regularity of 3D rotating Navier-Stokes equations for resonant domains. Indiana University Mathematics Journal 48 (1999) 1133-1176
5. Bardos C., Golse F., Mahalov A., and Nicolaenko B. Regularity of Euler equations for a class of three-dimensional initial data. Trends in Partial Differential Equations of Mathematical Physics. Progr. Nonlinear Differential Equations Appl. 61 (2005), Birkhäuser, Basel 161-185
6. Bresch D., and Desjardins B. Existence of global weak solutions for a 2D viscous shallow water equation and convergence to the quasi-geostrophic model. Commun. Math. Phys. 238 (2003) 211-223
7. Bresch D., Desjardins B., and Gérard-Varet D. Rotating fluids in a cylinder. Discrete and Contininous Dynamical Systems. 11 1 (2004) 47-82
8. D. Bresch, E. Grenier, D. Gérard-Varet, Derivation of the planetary geostrophic equations, Archive for Rational Mechanics and Analysis, to appear.
9. Bresch D., and Métivier G. Global existence and uniqueness for the lake equations with vanishing topography: elliptic estimates for degenerate equations (2005) Preprint
10. Charve F. Global well-posedness and asymptotics for a geophysical fluid system. Communications in Partial Differential Equations 29 (2004) 1919-1940
11. Charve F. Convergence of weak solutions for the primitive system of the quasigeostrophic equations. Asymptotic Analysis 42 (2005) 173-209
12. Chemin J.-Y., Desjardins B., Gallagher I., and Grenier E. Fluids with anisotropic viscosity. Modélisation Mathématique et Analyse Numérique 34 (2000) 315-335
13. Chemin J.-Y., Desjardins B., Gallagher I., and Grenier E. Basics of Mathematical Geophysics (2006), Oxford University Press to appear
14. Danchin R. Zero Mach number limit in critical spaces for compressible Navier-Stokes equations. Annales Scientifiques de l'École Normale Supérieure 35 1 (2002) 27-75
15. Danchin R. R. Zero Mach number limit for compressible flows with periodic boundary conditions. Amer. J. Math. 124 6 (2002) 1153-1219
16. Desjardins B., and Grenier E. Low Mach number limit of viscous compressible flows in the whole space. Proceedings of the Royal Society of London, Ser. A Math. Phys. Eng. Sci. 455 (1999) 2271-2279
17. Desjardins B., and Grenier E. On the homogeneous model of wind-driven ocean circulation. SIAM Journal on Applied Mathematics 60 (1999) 43-60
18. Desjardins B., Grenier E., Lions P.-L., and Masmoudi N. Incompressible limit for solutions of the isentropic Navier-Stokes equations with Dirichlet boundary conditions. Journal de Mathématiques Pures et Appliquées 78 (1999) 461-471
19. Fuglister F.C. Gulf Stream '60, Progress in Oceanography I (1963), Pergamon Press 265-383
20. Fujita H., and Kato T. On the Navier-Stokes initial value problem I. Archive for Rational Mechanics and Analysis 16 (1964) 269-315
21. Gallagher I. Applications of Schochet's methods to parabolic equations. Journal de Mathématiques Pures et Appliquées 77 (1998) 989-1054
22. Gallagher I. A Remark on smooth solutions of the weakly compressible Navier-Stokes equations. Journal of Mathematics of Kyoto University 40 (2000) 525-540
23. Gallagher I. Résultats récents sur la limite incompressible. (French) [Recent results on the incompressible limit]. Séminaire Bourbaki, Vol. 2003/2004. Astérisque No. 299 (2005) vii Exp. No. 926
24. Gallagher I. Résultats récents sur la limite incompressible. (French) [Recent results on the incompressible limit]. Séminaire Bourbaki, Vol. 2003/2004. Astérisque No. 299 (2005) 29-57
25. I. Gallagher and L. Saint-Raymond, Weak convergence results for inhomogeneous rotating fluid equations, Journal d'Analyse Mathématique, to appear.
26. Gallagher I., and Saint-Raymond L. Study of equatorial waves for the β-plane model (2006) Preprint
27. Gérard-Varet D. Highly rotating fluids in rough domains. Journal de Mathématiques Pures et Appliquées 82 (2003) 1453-1498
28. Gill A.E. Atmosphere-Ocean Dynamics, International Geophysics Series vol. 30 (1982)
29. Gill A.E., and Longuet-Higgins M.S. Resonant interactions between planetary waves. Proc. Roy. Soc. London A299 (1967) 120-140
30. Golse F., and Saint-Raymond L. The Vlasov-Poisson system with strong magnetic field. Journal de Mathématiques Pures et Appliquées 78 (1999) 791-817
31. Greenspan H.P. The Theory of Rotating Fluids. Cambridge monographs on mechanics and applied mathematics (1969)
32. Grenier E. Oscillatory perturbations of the Navier-Stokes equations. Journal de Mathématiques Pures et Appliquées 76 (1997) 477-498
33. Grenier E., and Masmoudi N. Ekman layers of rotating fluids, the case of well prepared initial data. Communications in Partial Differential Equations 22 5-6 (1997) 953-975
34. Joly J.-L., Métivier G., and Rauch J. Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves. Duke Mathematical Journal 70 (1993) 373-404
35. Joly J.-L., Métivier G., and Rauch J. Coherent and focusing multidimensional nonlinear geometric optics. Annales scientifiques de l'École Normale Supérieure 28 (1995) 51-113
36. Klein R., and Majda A. Systematic multi-scale models for the tropics. Journal of Atmospheric Sciences 60 (2003) 173-196
37. Leray J. Essai sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Matematica 63 (1933) 193-248
38. Leray J. Etude de diverses équations inté grales non linéaires et de quelques problèmes que pose l'hydrodynamique. Journal de Mathématiques Pures et Appliquées 12 (1933) 1-82
39. Lions J.-L., Temam R., and Wang S. New formulations of the primitive equations of atmosphere and applications. Nonlinearity 5 (1992) 237-288
40. Lions P.-L. Mathematical Topics in Fluid Mechanics, Vol. II, Compressible Models (1997), Oxford Science Publications
41. Lions P.-L., and Masmoudi N. Une approche locale de la limite incompressible. C. R. Acad. Sci. Paris Sér. I Math. 329 (1999) 387-392
42. Lions P.-L., and Masmoudi N. Incompressible limit for a viscous compressible fluid. Journal de Mathématiques Pures et Appliquées 77 (1998) 585-627
43. Majda A. Introduction to PDEs and Waves for the Atmosphere and Ocean. Courant Lecture Notes in Mathematics 9 (2003), New York University, Courant Institute of Mathematical Sciences, New York American Mathematical Society, Providence, RI
44. Majdoub M., and Paicu M. Uniform local existence for inhomogeneous rotating fluid equations (2005) Preprint
45. Masmoudi N. Ekman layers of rotating fluids: the case of general initial data. Communications in Pure and Applied Mathematics 53 (2000) 432-483
46. Masmoudi N. Some asymptotic problems in fluid mechanics. Evolution equations and their applications in physical and life sciences (Bad Herrenalb, 1998). Lecture Notes in Pure and Appl. Math. 215 (2001), Dekker, New York 395-404
47. Mellet A., and Vasseur A. On the isentropic compressible Navier-Stokes equation (2005) Preprint
48. Métivier G., and Schochet S. The incompressible limit of the non-isentropic Euler equations. Arch. Ration. Mech. Anal. 158 (2001) 61-90
49. M. Paicu, Equation anisotrope de Navier-Stokes dans des espaces critiques, Revista Matematica Iberoamericana, to appear.
50. Palmén E., and Newton C.W. Atmospheric Circulation Systems (1969), Academic Press
51. Pedlosky J. Geophysical Fluid Dynamics (1979), Springer
52. Philander S. El Nino, La Nina, and the Southern Oscillation (1990), Academic Press
53. Reed M., and Simon B. Methods of Modern Mathematical Physics, III, Scattering Theory (1979), Academic Press
54. Rousset F. Asymptotic behaviour of geophysical fluids in highly rotating balls (2004) Preprint
55. Schochet S. Fast singular limits of hyperbolic PDEs. Journal of Differential Equations 114 (1994) 476-512
56. (Lord Kelvin). Thomson W. On gravitational oscillations of rotating water. Proc. Roy. Soc. Edinburgh 10 (1879) 92-100
57. Temam R., and Ziane M. Some mathematical problems in geophysical fluid dynamics. In: Friedlander S., and Serre D. (Eds). Handbook of Mathematical Fluid Dynamics vol. III (2004) 535-657