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On the upper semicontinuity of pullback attractors for multi-valued noncompact random dynamical systems
The steady state solutions to thermohaline circulation equations
1. | College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, China, China |
References:
[1] |
H. Dijkstra and M. Ghil, Low-frequency variability of the large-scale ocean circulations: a dynamical system approach, Review of Geophysics, 43 (2005), 1-38.
doi: 10.1029/2002RG000122. |
[2] |
H. Dijkstra and M. Molemaker, Symmetry breaking and overturning oscillations in thermohaline-driven flows, J. Fluid Mech., 331 (1997), 195-232. |
[3] |
H. Dijkstra and J. Neclin, Imperfections of the thermohaline circulation: Multiple equilibria and flux correction, Journal of Climate, 12 (1999), 1382-1392.
doi: 10.1175/1520-0442(1999)012<1382:IOTTCM>2.0.CO;2. |
[4] |
L. Evans, Partial Differential Equations, American Mathematical Society, Rhode Island, 1998. |
[5] |
C. Foias and R. Temam, Structure of the set of stationary solutions of the Navier-Stokes equations, Communications on Pure and Applied Mathematics, 30 (1977), 149-164.
doi: 10.1002/cpa.3160300202. |
[6] |
Y. G. Gu and W. J Sun, Nontrivial equilibrium solutions for a semilinear reaction diffusion system, Applied Mathematics and Mechanics, 25 (2004), 1382-1389.
doi: 10.1007/BF02438295. |
[7] |
S. Henry and P. Hall, Thermohaline convection with two stable regimes of flow, Tellus, 13 (1961), 224-230. |
[8] |
Z. J. Jiang and S. L. Sun, Functional Analysis, (Chinese)Higher Education Press, China, 2005. |
[9] |
H. Luo, Steady state solution to atmospheric circulation equations with humidity effect, Journal of Applied Mathematics, 2012 (2012), Art. ID 867310, 18 pp. |
[10] |
T. Ma and S. H. Wang, Dynamic transition theory for thermohaline circulation, Physical D, 239 (2010), 167-189.
doi: 10.1016/j.physd.2009.10.014. |
[11] |
T. Ma and S. H. Wang, Stability and Bifurcation of Nonlinear Evolution Equations, (Chinese) Science Press, Beijing, China, 2007. |
[12] |
T. Ma and S. H. Wang, Bifurcation Theory and Applications, Nonl. Sci. Ser. A, World Scientific, 2005.
doi: 10.1142/5798. |
[13] |
T. Ma, Theories and Methods in Partial Differential Equations, (Chinese) Science Press, China, 2011. |
[14] |
R. Sell G and Y. C. You, Dynamics of Evolutionary Equations, Applied Mathematical Sciences, 143, Springer-Verlag, New York, 2002. |
[15] |
R. Temam, Navier-Stokes Equation and Nonlinear Functional Analysis, $2^{nd}$ edition, CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 1983. |
[16] |
R. Temam, Navier-Stokes equation: Theory and Numerical Analysis, North-Holland Publishing Co., Amsterdam, The Netherlands, 1979. |
[17] |
R. Temam, Infinite-dimensional Dynamical Systems In Mechanics And Physics, Applied Mathematics and Science, Vol. 68, New York, Springer, 1997.
doi: 10.1007/978-1-4612-0645-3. |
[18] |
O. Thual and J. McWilliams, The Catastrophe structure of thermohaline convection in a two-dimensional fluid model and a comparison with low-order box models, Geophysical Astrophysical Fluid Dynamics, 64 (1992), 67-95.
doi: 10.1080/03091929208228085. |
[19] |
E. Tziperman, J. Toggweiler, Y. Fzliks and K. Bryan, Instability of the thermohaline circulation with respect to mixed boundary conditions: Is it really a problem for realistic models?, Journal of Physical Oceanography, 24 (1994), 217-232.
doi: 10.1175/1520-0485(1994)024<0217:IOTTCW>2.0.CO;2. |
show all references
References:
[1] |
H. Dijkstra and M. Ghil, Low-frequency variability of the large-scale ocean circulations: a dynamical system approach, Review of Geophysics, 43 (2005), 1-38.
doi: 10.1029/2002RG000122. |
[2] |
H. Dijkstra and M. Molemaker, Symmetry breaking and overturning oscillations in thermohaline-driven flows, J. Fluid Mech., 331 (1997), 195-232. |
[3] |
H. Dijkstra and J. Neclin, Imperfections of the thermohaline circulation: Multiple equilibria and flux correction, Journal of Climate, 12 (1999), 1382-1392.
doi: 10.1175/1520-0442(1999)012<1382:IOTTCM>2.0.CO;2. |
[4] |
L. Evans, Partial Differential Equations, American Mathematical Society, Rhode Island, 1998. |
[5] |
C. Foias and R. Temam, Structure of the set of stationary solutions of the Navier-Stokes equations, Communications on Pure and Applied Mathematics, 30 (1977), 149-164.
doi: 10.1002/cpa.3160300202. |
[6] |
Y. G. Gu and W. J Sun, Nontrivial equilibrium solutions for a semilinear reaction diffusion system, Applied Mathematics and Mechanics, 25 (2004), 1382-1389.
doi: 10.1007/BF02438295. |
[7] |
S. Henry and P. Hall, Thermohaline convection with two stable regimes of flow, Tellus, 13 (1961), 224-230. |
[8] |
Z. J. Jiang and S. L. Sun, Functional Analysis, (Chinese)Higher Education Press, China, 2005. |
[9] |
H. Luo, Steady state solution to atmospheric circulation equations with humidity effect, Journal of Applied Mathematics, 2012 (2012), Art. ID 867310, 18 pp. |
[10] |
T. Ma and S. H. Wang, Dynamic transition theory for thermohaline circulation, Physical D, 239 (2010), 167-189.
doi: 10.1016/j.physd.2009.10.014. |
[11] |
T. Ma and S. H. Wang, Stability and Bifurcation of Nonlinear Evolution Equations, (Chinese) Science Press, Beijing, China, 2007. |
[12] |
T. Ma and S. H. Wang, Bifurcation Theory and Applications, Nonl. Sci. Ser. A, World Scientific, 2005.
doi: 10.1142/5798. |
[13] |
T. Ma, Theories and Methods in Partial Differential Equations, (Chinese) Science Press, China, 2011. |
[14] |
R. Sell G and Y. C. You, Dynamics of Evolutionary Equations, Applied Mathematical Sciences, 143, Springer-Verlag, New York, 2002. |
[15] |
R. Temam, Navier-Stokes Equation and Nonlinear Functional Analysis, $2^{nd}$ edition, CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 1983. |
[16] |
R. Temam, Navier-Stokes equation: Theory and Numerical Analysis, North-Holland Publishing Co., Amsterdam, The Netherlands, 1979. |
[17] |
R. Temam, Infinite-dimensional Dynamical Systems In Mechanics And Physics, Applied Mathematics and Science, Vol. 68, New York, Springer, 1997.
doi: 10.1007/978-1-4612-0645-3. |
[18] |
O. Thual and J. McWilliams, The Catastrophe structure of thermohaline convection in a two-dimensional fluid model and a comparison with low-order box models, Geophysical Astrophysical Fluid Dynamics, 64 (1992), 67-95.
doi: 10.1080/03091929208228085. |
[19] |
E. Tziperman, J. Toggweiler, Y. Fzliks and K. Bryan, Instability of the thermohaline circulation with respect to mixed boundary conditions: Is it really a problem for realistic models?, Journal of Physical Oceanography, 24 (1994), 217-232.
doi: 10.1175/1520-0485(1994)024<0217:IOTTCW>2.0.CO;2. |
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