December  2016, 21(10): 3709-3722. doi: 10.3934/dcdsb.2016117

The steady state solutions to thermohaline circulation equations

1. 

College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, China, China

Received  December 2015 Revised  May 2016 Published  November 2016

In the article, we study the existence and the regularity of the steady state solutions to thermohaline circulation equations. Firstly, we obtain a sufficient condition of the existence of weak solutions to the equations by acute angle theory of weakly continuous operator. Secondly, we prove the existence of strong solutions to the equations by ADN theory and iteration procedure. Furthermore, we study the generic property of the solutions by Sard-Smale theorem and the existence of classical solutions by ADN theorem.
Citation: Chao Xing, Ping Zhou, Hong Luo. The steady state solutions to thermohaline circulation equations. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3709-3722. doi: 10.3934/dcdsb.2016117
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show all references

References:
[1]

Review of Geophysics, 43 (2005), 1-38. doi: 10.1029/2002RG000122.  Google Scholar

[2]

J. Fluid Mech., 331 (1997), 195-232. Google Scholar

[3]

Journal of Climate, 12 (1999), 1382-1392. doi: 10.1175/1520-0442(1999)012<1382:IOTTCM>2.0.CO;2.  Google Scholar

[4]

American Mathematical Society, Rhode Island, 1998.  Google Scholar

[5]

Communications on Pure and Applied Mathematics, 30 (1977), 149-164. doi: 10.1002/cpa.3160300202.  Google Scholar

[6]

Applied Mathematics and Mechanics, 25 (2004), 1382-1389. doi: 10.1007/BF02438295.  Google Scholar

[7]

Tellus, 13 (1961), 224-230. Google Scholar

[8]

(Chinese)Higher Education Press, China, 2005. Google Scholar

[9]

Journal of Applied Mathematics, 2012 (2012), Art. ID 867310, 18 pp.  Google Scholar

[10]

Physical D, 239 (2010), 167-189. doi: 10.1016/j.physd.2009.10.014.  Google Scholar

[11]

(Chinese) Science Press, Beijing, China, 2007. Google Scholar

[12]

Nonl. Sci. Ser. A, World Scientific, 2005. doi: 10.1142/5798.  Google Scholar

[13]

(Chinese) Science Press, China, 2011. Google Scholar

[14]

Applied Mathematical Sciences, 143, Springer-Verlag, New York, 2002. Google Scholar

[15]

$2^{nd}$ edition, CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 1983.  Google Scholar

[16]

North-Holland Publishing Co., Amsterdam, The Netherlands, 1979.  Google Scholar

[17]

Applied Mathematics and Science, Vol. 68, New York, Springer, 1997. doi: 10.1007/978-1-4612-0645-3.  Google Scholar

[18]

Geophysical Astrophysical Fluid Dynamics, 64 (1992), 67-95. doi: 10.1080/03091929208228085.  Google Scholar

[19]

Journal of Physical Oceanography, 24 (1994), 217-232. doi: 10.1175/1520-0485(1994)024<0217:IOTTCW>2.0.CO;2.  Google Scholar

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