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The finite dimensional global attractor for the 3D viscous Primitive Equations
1. | Department of Mathematics, Oklahoma State University, 401 Mathematical Sciences, Stillwater, OK 74078 |
References:
[1] |
C. Cao and E. S. Titi, Global well-posedness and finite dimensional global attractor for a 3-D planetary geostrophic viscous model, Comm. Pure Appl. Math., 56 (2003), 198-233.
doi: 10.1002/cpa.10056. |
[2] |
C. Cao and E. S. Titi, Global well-posedness of the three-dimensional primitive equations of large scale ocean and atmosphere dynamics, Ann. of Math.(2), 166 (2007), 245-267.
doi: 10.4007/annals.2007.166.245. |
[3] |
I. Chueshov, A squeezing property and its applications to a description of long time behaviour in the 3D viscous primitive equations, Proc. Roy. Soc. Edinburgh Sect. A, 144 (2014), 711-729.
doi: 10.1017/S0308210512001953. |
[4] |
P. Constantin, C. Foias and R. Temam, Attractors representing turbulent flows, Memoirs of A.M.S., 53 (1985), vii+67 pp.
doi: 10.1090/memo/0314. |
[5] |
L. Evans and R. Gastler, Some results for the primitive equations with physical boundary conditions, Z. Angew. Math. Phys., 64 (2013), 1729-1744.
doi: 10.1007/s00033-013-0320-6. |
[6] |
F. Guillén-Gonzáez, N. Masmoudi and M. A. Rodríguez-Bellido, Anisotropic estimates and strong solutions of the primitive equations, Diff. Integral Eq., 14 (2001), 1381-1408. |
[7] |
N. Ju, The global attractor for the solutions to the 3D viscous primitive equations, Discrete and Continuous Dynamical Systems, 17 (2007), 159-179.
doi: 10.3934/dcds.2007.17.159. |
[8] |
N. Ju and R. Temam, Finite dimensions of the global attractor for 3D primitive equations with viscosity, J. Nonlinear Sci., 25 (2015), 131-155.
doi: 10.1007/s00332-014-9223-8. |
[9] |
G. Kobelkov, Existence of a solution 'in the large' for the 3D large-scale ocean dynamics equations, C. R. Math. Acad. Sc. Paris, 343 (2006), 283-286.
doi: 10.1016/j.crma.2006.04.020. |
[10] |
G. Kobelkov, Existence of a solution 'in the large' for ocean dynamics equations, J. Math. Fluid Mech., 9 (2007), 588-610.
doi: 10.1007/s00021-006-0228-4. |
[11] |
I. Kukavica and M. Ziane, On the regularity of the primitive equations of the ocean, Nonlinearity, 20, (2007), 2739-2753.
doi: 10.1088/0951-7715/20/12/001. |
[12] |
I. Kukavica and M. Ziane, Uniform gradient bounds for the primitive equations of the ocean, Differential Integral Equations, 21 (2008), 837-849. |
[13] |
O. Ladyzhenskaya, Some comments to my papers on the theory of attractors for abstract semigroups, Zap. Nauchn. Sem. LOMI, 182 (1990), 102-112; English translation in J. Soviet Math., 62 (1992), 2789-2794.
doi: 10.1007/BF01671002. |
[14] |
J. L. Lions, R. Temam and S. Wang, New formulations of the primitive equations of atmosphere and applications, Nonlinearity, 5 (1992), 237-288.
doi: 10.1088/0951-7715/5/2/001. |
[15] |
J. Lions, R. Temam and S. Wang, On the equations of the large scale Ocean, Nonlinearity, 5 (1992), 1007-1053.
doi: 10.1088/0951-7715/5/5/002. |
[16] |
M. Petcu, On the three dimensional primitive equations, Adv. Dif. Eq., 11 (2006), 1201-1226. |
[17] |
R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics, Applied Mathematical Sciences, 68. Springer-Verlag, New York, 1988.
doi: 10.1007/978-1-4684-0313-8. |
[18] |
R. Temam, Navier-Stokes equations. Theory and numerical analysis, reprint of 3rd edition, American Mathematical Society 2001.
doi: 10.1090/chel/343. |
[19] |
R. Temam and M. Ziane, Some mathematical problems in geophysical fluid dynamics, Handbook of Mathematical Fluid Dynamics, 3 (2004), 535-657. |
show all references
References:
[1] |
C. Cao and E. S. Titi, Global well-posedness and finite dimensional global attractor for a 3-D planetary geostrophic viscous model, Comm. Pure Appl. Math., 56 (2003), 198-233.
doi: 10.1002/cpa.10056. |
[2] |
C. Cao and E. S. Titi, Global well-posedness of the three-dimensional primitive equations of large scale ocean and atmosphere dynamics, Ann. of Math.(2), 166 (2007), 245-267.
doi: 10.4007/annals.2007.166.245. |
[3] |
I. Chueshov, A squeezing property and its applications to a description of long time behaviour in the 3D viscous primitive equations, Proc. Roy. Soc. Edinburgh Sect. A, 144 (2014), 711-729.
doi: 10.1017/S0308210512001953. |
[4] |
P. Constantin, C. Foias and R. Temam, Attractors representing turbulent flows, Memoirs of A.M.S., 53 (1985), vii+67 pp.
doi: 10.1090/memo/0314. |
[5] |
L. Evans and R. Gastler, Some results for the primitive equations with physical boundary conditions, Z. Angew. Math. Phys., 64 (2013), 1729-1744.
doi: 10.1007/s00033-013-0320-6. |
[6] |
F. Guillén-Gonzáez, N. Masmoudi and M. A. Rodríguez-Bellido, Anisotropic estimates and strong solutions of the primitive equations, Diff. Integral Eq., 14 (2001), 1381-1408. |
[7] |
N. Ju, The global attractor for the solutions to the 3D viscous primitive equations, Discrete and Continuous Dynamical Systems, 17 (2007), 159-179.
doi: 10.3934/dcds.2007.17.159. |
[8] |
N. Ju and R. Temam, Finite dimensions of the global attractor for 3D primitive equations with viscosity, J. Nonlinear Sci., 25 (2015), 131-155.
doi: 10.1007/s00332-014-9223-8. |
[9] |
G. Kobelkov, Existence of a solution 'in the large' for the 3D large-scale ocean dynamics equations, C. R. Math. Acad. Sc. Paris, 343 (2006), 283-286.
doi: 10.1016/j.crma.2006.04.020. |
[10] |
G. Kobelkov, Existence of a solution 'in the large' for ocean dynamics equations, J. Math. Fluid Mech., 9 (2007), 588-610.
doi: 10.1007/s00021-006-0228-4. |
[11] |
I. Kukavica and M. Ziane, On the regularity of the primitive equations of the ocean, Nonlinearity, 20, (2007), 2739-2753.
doi: 10.1088/0951-7715/20/12/001. |
[12] |
I. Kukavica and M. Ziane, Uniform gradient bounds for the primitive equations of the ocean, Differential Integral Equations, 21 (2008), 837-849. |
[13] |
O. Ladyzhenskaya, Some comments to my papers on the theory of attractors for abstract semigroups, Zap. Nauchn. Sem. LOMI, 182 (1990), 102-112; English translation in J. Soviet Math., 62 (1992), 2789-2794.
doi: 10.1007/BF01671002. |
[14] |
J. L. Lions, R. Temam and S. Wang, New formulations of the primitive equations of atmosphere and applications, Nonlinearity, 5 (1992), 237-288.
doi: 10.1088/0951-7715/5/2/001. |
[15] |
J. Lions, R. Temam and S. Wang, On the equations of the large scale Ocean, Nonlinearity, 5 (1992), 1007-1053.
doi: 10.1088/0951-7715/5/5/002. |
[16] |
M. Petcu, On the three dimensional primitive equations, Adv. Dif. Eq., 11 (2006), 1201-1226. |
[17] |
R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics, Applied Mathematical Sciences, 68. Springer-Verlag, New York, 1988.
doi: 10.1007/978-1-4684-0313-8. |
[18] |
R. Temam, Navier-Stokes equations. Theory and numerical analysis, reprint of 3rd edition, American Mathematical Society 2001.
doi: 10.1090/chel/343. |
[19] |
R. Temam and M. Ziane, Some mathematical problems in geophysical fluid dynamics, Handbook of Mathematical Fluid Dynamics, 3 (2004), 535-657. |
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