References
- Temam , R . 1988 . Infinite-dimensional Dynamical Systems in Mechanics and Physics, 2nd ed., Applications in Mathematical Sciences , Vol. 68 , New York : Springer-Verlag .
- Temam , R . 2001 . Navier–Stokes Equations, Theory and Numerical Analysis , Providence : AMS-Chelsea Series, AMS .
- Bernier , C . 1994 . Existence of attractor for the quasi-geostrophic approximation of the Navier–Stokes equations and estimate of its dimension . Adv. Math. Sci. Appl. , 4 ( 2 ) : 465 – 489 .
- Ju , N . 2007 . The global attractor for the solutions to the 3D viscous primitive equations . Discr. Contin. Dyn. Syst. , 17 ( 1 ) : 159 – 179 .
- Cao , C and Titi , ES . 2003 . Global well-posedness and finite-dimensional global attractor for a 3-D planetary geostrophic viscous model . Comm. Pure Appl. Math. , 56 ( 2 ) : 198 – 233 .
- Samelson , R , Temam , R and Wang , S . 1998 . Some mathematical properties of the planetary geostrophic equations for large-scale ocean circulation . Appl. Anal , 70 ( 1–2 ) : 147 – 173 .
- Caraballo , T and Real , J . 2003 . Asymptotic behaviour of two-dimensional Navier–Stokes equations with delays . R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. , 459 ( 2040 ) : 3181 – 3194 .
- Caraballo , T and Real , J . 2004 . Attractors for 2D Navier–Stokes models with delays . J. Differ. Eqns , 205 ( 2 ) : 271 – 297 .
- Crauel , H , Debussche , A and Flandoli , F . 1995 . Random attractors . J. Dyn. Differ. Eqns , 2 ( 2 ) : 307 – 341 .
- Kloeden , PE and Schmalfuss , B . 1997 . Nonautonomous systems, cocycle attractors and variable time-step discretization . Numer. Algorithms , 14 : 141 – 152 .
- Kloeden , PE and Stonier , DJ . 1998 . Cocycle attractors in nonautonomously perturbed differential equations . Dyn. Contin. Impulsive Syst. , 4 ( 2 ) : 211 – 226 .
- Lions , JL , Temam , R and Wang , S . 1992 . New formulations of the primitive equations of the atmosphere and applications . Nonlinearity , 5 : 237 – 288 .
- Lions , JL , Temam , R and Wang , S . 1992 . On the equations of large-scale ocean . Nonlinearity , 5 : 1007 – 1053 .
- Chepyzhov , VV , Pata , V and Vishik , MI . 2009 . Averaging of 2D Navier–Stokes equations with singularly oscillating forces . Nonlinearity , 22 ( 2 ) : 351 – 370 .
- Chepyzhov , VV , Pata , V and Vishik , MI . 2008 . Averaging of nonautonomous damped wave equations with singularly oscillating external forces . J. Math. Pures Appl. (9) , 90 ( 5 ) : 469 – 491 .
- Chepyzhov , VV and Vishik , MI . 2007 . Non-autonomous 2D Navier–Stokes system with singularly oscillating external force and its global attractor . J. Dyn. Differ. Eqns , 19 ( 3 ) : 655 – 684 .
- Chepyzhov , VV and Vishik , MI . 2002 . “ Attractors for Equations of Mathematical Physics ” . In American Mathematical Society Colloquium Publications , Vol. 49 , Providence , , RI : American Mathematical Society .
- Chepyzhov , VV , Pata , V and Vishik , MMI . 2009 . Averaging of 2D Navier–Stokes equations with singularly oscillating forces . Nonlinearity , 22 : 351 – 370 .
- Chepyzhov , VV and Vishik , MMI . 2001 . Averaging of trajectory attractors of evolution equations with rapidly oscillating terms . Sb. Math , 192 ( 1–2 ) : 11 – 47 .
- Cheskidov , A and Lu , S . 2009 . The existence and the structure of uniform global attractors for nonautonomous reaction–diffusion systems without uniqueness . Discr. Contin. Dyn. Syst. Ser. S , 2 ( 1 ) : 55 – 66 .
- Lu , S . 2006 . Attractors for nonautonomous 2D Navier–Stokes equations with less regular normal forces . J. Differ. Eqns , 230 ( 1 ) : 196 – 212 .
- Lu , S , Wu , H and Zhong , C . 2005 . Attractors for nonautonomous 2D Navier–Stokes equations with normal external forces . Discr. Contin. Dyn. Syst. , 13 ( 3 ) : 701 – 719 .
- Song , H , Ma , S and Zhong , C . 2009 . Attractors of non-autonomous reaction–diffusion equations . Nonlinearity , 22 ( 3 ) : 667 – 681 .
- Wang , Y and Zhong , C . 2008 . On the existence of pullback attractors for non-autonomous reaction-diffusion equations . Dyn. Syst. , 23 ( 1 ) : 1 – 16 .
- Caraballo , T and Kloeden , PE . 2009 . Non-autonomous attractor for integro-differential evolution equations . Disc. Contin. Dyn. Syst. Ser. S , 2 ( 1 ) : 17 – 36 .
- Haraux , A . 1991 . “ Systèmes Dynamiques Dissipatifs et Applications ” . In Recherches en Mathématiques Appliquées , Vol. 17 , Paris : Mason .
- Babin , AV and Vishik , MI . 1992 . “ Attractors of Evolution Equations ” . In Studies in Mathematics and its Applications , Vol. 25 , Amsterdam : North-Holland Publishing Co .
- Chepyzhov , VV and Vishik , MMI . Averaging of trajectory attractors of evolution equations with rapidly oscillating coefficients. Funct. Differ. Eqns. 8(1–2) (2001), pp. 123–140
- Chepyzhov , VV , Vishik , MI and Wendland , WL . 2005 . On non-autonomous Sine-Gordon type equations with a simple global attractor and some averaging . Discr. Contin. Dyn. Syst. , 12 ( 1 ) : 27 – 38 .
- Lions , JL , Temam , R and Wang , S . 1993 . Models of the coupled atmosphere and ocean (CAO I) . Comput. Mech. Adv. , 1 : 3 – 54 .
- Lions , JL , Temam , R and Wang , S . 1993 . Numerical analysis of the coupled atmosphere and ocean models (CAOII) . Comput. Mech. Adv. , 1 : 55 – 120 .
- Lions , JL , Temam , R and Wang , S . 1995 . Mathematical study of the coupled models of atmosphere and ocean (CAOIII) . Math. Pures Appl. , 73 : 105 – 163 .
- Lions , JL , Temam , R and Wang , S . 2000 . On mathematical problems for the primitive equations of the ocean: the mesoscale midlatitude case. Lakshmikantham's legacy: A tribute on his 75th birthday . Nonlinear Anal. Ser. A. Theory Methods , 40 ( 1–8 ) : 439 – 482 .
- Simmonet , E , Tachim Medjo , T and Temam , R . 2003 . Barotropic-baroclinic formulation of the primitive equations of the ocean . Appl. Anal. , 82 ( 5 ) : 439 – 456 .
- Wang , S . 1988 . “ On solvability for the equations of the large-scale atmospheric motion ” . In PhD thesis , China : Lanzhou University .
- Cao , C and Titi , ES . 2007 . Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics . Ann. Math. (2) , 166 ( 1 ) : 245 – 267 .
- Hu , C , Temam , R and Ziane , M . 2002 . Regularity results for linear elliptic problems related to the primitive equations . Chin. Ann. Math. , 23B ( 2 ) : 1 – 16 .
- Hu , C , Temam , R and Ziane , M . 2003 . The primitive equations of the large scale ocean under the small depth hypothesis . Discr. Contin. Dyn. Syst. , 9 ( 1 ) : 97 – 131 .
- Hu , C . 2005 . Asymptotic analysis of the primitive equations under the small depth assumption . Nonlinear Anal. , 61 ( 3 ) : 425 – 460 .
- Haltiner , GJ and Williams , RT . 1980 . Numerical Prediction and Dynamic Meteorology , New York : John Wiley and Sons .
- Pedlosky , J . 1987 . Geophysical Fluid Dynamics , 2nd , New York : Springer-Verlag .
- Peixoto , JP and Oort , AH . 1992 . Physics of Climate , New York : American Institute of Physics .
- Washington , WM and Parkinson , CL . 1986 . An Introduction to Three-dimensional Climate Modeling , Oxford : Oxford University Press .
- Tachim Medjo , T . 2011 . Non-autonomous planetary 3D geostrophic equations with oscillating external force and its global attractor . Nonlinear Anal. Real World Appl. , 12 ( 3 ) : 1437 – 1452 .
- Kobelkov , GM . 2006 . Existence of a solution ‘in the large’ for the 3D large-scale ocean dynamics equations . C. R. Math. Acad. Sci. Paris , 343 : 283 – 286 .
- Tachim Medjo , T . 2010 . On the uniqueness of z-weak solutions of the three-dimensional primitive equations of the ocean . Nonlinear Anal. Real World Appl. , 11 ( 3 ) : 1413 – 1421 .
- Tachim Medjo , T . 2012 . Non-autonomous 3D primitive equations with oscillating external force and its global attractor . Discr. Contin. Dyn. Syst. , 32 ( 1 ) : 265 – 291 .