Abstract
In this article we present the classical primitive equations of the atmosphere, of the ocean, and of the coupled atmosphere and ocean. We also summarize a number of results concerning the well-posedness of the associated boundary and initial value problems, and concerning the long time behavior of the solutions (attractors and dynamical systems points of views).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
V. Bjerknes, Das Problem von der Wettervorhersage, betrachtet vom Standpunkt der Mechanik und der der Physik., Meteor. Z., 21 (1904), 1–7.
J.G. Charney, The dynamics of long waves in a baroclinic westerly current. J. Meteorol, 4 (1947), 135–163.
C. Foias, O. Manley, R. Rosa and R. Temam (2001), Turbulence and Navier-Stokes Equations, Cambridge University Press, to appear.
A.E. Gill (1982), Atmosphere-Ocean Dynamics, (Academic Press, New York).
G. Haitiner and R. Williams (1980), Numerical Weather Prediction and Dynamic Meteorology, (2nd ed., Wiley, New York).
C. Hu, R. Temam and M. Ziane (2000), Articles in preparation.
J.L. Lions, O. Manley, R. Temam and S. Wang, Physical interpretation of the attractor for a simple model of atmospheric circulation. Journal of the Atmospheric Sciences, 54 (1997), No. 9, 1137–1143.
J.L. Lions, R. Temam and S. Wang, New Formulations of the Primitive Equations of the Atmosphere and Applications. Nonlinearity, 5 (1992a), 237–288.
J.L. Lions, R. Temam and S. Wang, On the equations of large-scale ocean. Nonlinearity, 5 (1992b), 1007–1053.
J.L. Lions, R. Temam and S. Wang, Models of the Coupled Atmosphere and Ocean. Computational Mechanics Advances, 1 (1993), 5–54 and 55-119.
J.L. Lions, R. Temam and S. Wang, Mathematical study of the coupled models of atmosphere and ocean (CAO III). J. Math. Pures Appl., 74 (1995), 105–163.
G.I. Marchuk and A.S. Sarkisyan (1988), Mathematical modelling of ocean circulation. Translated from the Russian by L.I. Egorova. Springer-Verlag, Berlin-New York.
J. Pedlosky (1987), Geophysical Fluid Dynamics, 2nd Edition, Springer-Verlag, New York.
P.H. Rabinowitz, Some aspects of nonlinear eigenvalue problems. Rocky Mountain J. Math., 3 (1973), 161–202.
G. Raugel and G.R. Sell, Navier-Stokes equations on thin 3D domains. I. Global attractors and global regularity of solutions. J. Amer. Math. Soc, 6 (1993), No. 3, 503–568.
G. Raugel and G.R. Sell, Navier-Stokes equations on thin 3D domains. II. Global regularity of spatially periodic solutions, Nonlinear partial differential equations and their applications. College de France Seminar, Vol. XI Pitman Res. Notes Math. Ser., 299 (1994), 205–247.
H. Schlichting (1979), Boundary layer theory, Translated by J. Kestin, 7th ed. McGraw Hill Series in Mechanical Engineering, McGraw Hill Book Co., Inc., New York.
S.H. Schneider (1996), Encyclopedia of Climate and Weather, Oxford University Press, Oxford.
R. Temam and M. Ziane, Navier-Stokes equations in three-dimensional thin domains with various boundary conditions, Adv. Differential Equations, 1 (1996), No. 4, 499–546.
R. Temam and M. Ziane, Navier-Stokes equations in thin spherical domains. Contemporary Mathematics, AMS, 209 (1997), 281–314.
K.E. Trenberth (1992), Climate System Modeling, Cambridge University Press, Cambridge.
W.M. Washington and C.L. Parkinson (1986), An Introduction to Three-Dimensional Climate Modeling, (Oxford University Press, Oxford, New York).
Q.C. Zeng (1979), Mathematical and Physical Foundations of Numerical Weather Prediction, Science Press, Beijing (in Chinese).
M. Ziane, Regularity results for Stokes type problems. Applicable Analysis, 58 (1995), 263–292.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Basel AG
About this paper
Cite this paper
Temam, R. (2001). Some mathematical aspects of the GCMs. In: Imkeller, P., von Storch, JS. (eds) Stochastic Climate Models. Progress in Probability, vol 49. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8287-3_4
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8287-3_4
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9504-0
Online ISBN: 978-3-0348-8287-3
eBook Packages: Springer Book Archive