Attractors for the multilayer quasi-geostrophic equations of the ocean with delays

References

• Colin , T . 1997 . The cauchy problem and the continuous limit for the multilayer model in geophysical fluid dynamics . SIAM J. Math. Anal. , 28 ( 3 ) : 516 – 529 .
   Google Scholar
• 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 .
   Google Scholar
• Bernier-Kazantsev , C and Chueshov , ID . 2000 . The finiteness of determining degrees of freedom for the quasi-geostrophic multilayer ocean model . Nonlinear Anal. , 42 : 1499 – 1512 .
   Google Scholar
• Caraballo , T and Real , J . 2001 . Navier-stokes equations with delays . R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. , 457 ( 2014 ) : 2441 – 2453 .
   Google Scholar
• 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 .
   Google Scholar
• Caraballo , T and Real , J . 2004 . Attractors for 2D-navier-stokes models with delays . J. Diff. Equat. , 205 ( 2 ) : 271 – 297 .
   Web of Science ®Google Scholar
• Caraballo , T , Márquez-Durán , AM and Real , J . 2006 . Pullback and forward attractors for a 3D LANS-α model with delay . Discrete Contin. Dyn. Syst. , 4 ( 2 ) : 559 – 578 .
   Google Scholar
• Kloeden , PE and Schmalfuss , B . 1997 . Nonautonomous systems, cocycle attractors and variable time-step discretization . Numer. Algorithms , 14 : 141 – 152 .
   Web of Science ®Google Scholar
• Kloeden , PE and Stonier , DJ . 1998 . Cocycle attractors in nonautonomously perturbed differential equations . Dyn. Contin. Impul. Syst. , 4 ( 2 ) : 211 – 226 .
   Google Scholar
• Crauel , H , Debussche , A and Flandoli , F . 1995 . Random attractors . J. Dyn. Diff. Equat. , 2 ( 2 ) : 307 – 341 .
   Google Scholar
• Lions , JL , Temam , R and Wang , S . 1992 . On the equations of large-scale ocean . Nonlinearity , 5 : 1007 – 1053 .
   Web of Science ®Google Scholar
• Lions , JL , Temam , R and Wang , S . 1993 . Models of the coupled atmosphere and ocean (CAO I) . Comput. Mech. Advance , 1 : 3 – 54 .
   Google Scholar
• Lions , JL , Temam , R and Wang , S . 1993 . Numerical analysis of the coupled atmosphere and ocean models (CAOII) . Comput. Mech. Advance , 1 : 55 – 120 .
   Google Scholar
• Lions , JL , Temam , R and Wang , S . 1995 . Mathematical study of the coupled models of atmosphere and ocean (CAOIII) . Math. Pures et Appl. , 73 : 105 – 163 .
   Google Scholar
• 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 .
   Google Scholar
• 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 .
   Google Scholar
• Hu , C , Temam , R and Ziane , M . 2003 . The primitive equations of the large scale ocean under the small depth hypothesis . Discrete Contin. Dyn. Syst. , 9 ( 1 ) : 97 – 131 .
   Web of Science ®Google Scholar
• Hu , C . 2005 . Asymptotic analysis of the primitive equations under the small depth assumption . Nonlinear Anal. , 61 ( 3 ) : 425 – 460 .
   Google Scholar
• 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 .
   Google Scholar
• Tachim Medjo , T . 2005 . Barotropic-baroclinic time splitting for the primitive equations of the ocean . Multiscale Model. Simul. , 4 ( 1 ) : 194 – 212 .
   Google Scholar
• Tachim Medjo , T , Temam , R and Wang , S . 1997 . High order approximation equations for the primitive equations of the atmosphere . J. Engrg. Math., Special issue on Large-Scale Numerical Modeling of Problems involving the Navier-Stokes equations. , 32 : 237 – 256 .
   Google Scholar
• Haltiner , GJ and Williams , RT . 1980 . Numerical Prediction and Dynamic Meteorology , New York : John Wiley and Sons .
   Google Scholar
• Pedlosky , J . 1987 . Geophysical Fluid Dynamics , 2nd , New-York : Springer-Verlag .
   Google Scholar
• Peixoto , JP and Oort , AH . 1992 . Physics of Climate , New-York : American Institute of Physics .
   Google Scholar
• Washington , WM and Parkinson , CL . 1986 . An Introduction to Three-Dimensional Climate Modeling , Oxford : Oxford University Press .
   Google Scholar
• Temam , R . 1988 . “ Infinite Dimensional Dynamical Systems in Mechanics and Physics ” . In Appl. Math. Sci. , 2nd , Vol. 68 , New York : Springer-Verlag .
   Google Scholar
• Temam , R . 2001 . Navier-Stokes Equations, Theory and Numerical Analysis , AMS, Providence : AMS-Chelsea Series .
   Google Scholar
• Ju , N . 2007 . The global attractor for the solutions to the 3D viscous primitive equations . Discrete Contin. Dyn. Syst. , 17 ( 1 ) : 159 – 179 .
   Google Scholar
• 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 .
   Google Scholar
• 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 .
   Google Scholar
• Lions , JL , Temam , R and Wang , S . 1992 . New formulations of the primitive equations of the atmosphere and applications . Nonlinearity, , 5 : 237 – 288 .
   Web of Science ®Google Scholar
• Tachim Medjo , T . 2007 . On strong solutions of the multilayer quasi-geostrophic equations of the ocean . Accepted in Nonlinear Anal. , accepted
   Google Scholar
• Agoshkov , VI and Ipatova , VM . 1997 . Solvability of the altimeter data assimilation problem in the quasi-geostrophic multilayer moldel of ocean circulation . Comput. Math. Math. Phys. , 37 ( 3 ) : 348 – 358 .
   Google Scholar
• Tachim Medjo , T . 2007 . multilayer quasi-geostrophic equations of the ocean with delays . accepted Disc. and Cont. Dyn. Syst., Ser. B ,
   Google Scholar