# American Institute of Mathematical Sciences

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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