热盐环流方程的渐近理论

发布时间：2018-08-25 10:50

【摘要】：本文研究了热盐环流方程稳态解以及弱吸引子的存在性,包含以下三个部分.第一部分,研究了热盐环流方程稳态解的存在性与正则性.首先,利用弱连续算子的锐角原理,研究了热盐环流方程稳态弱解的存在性.其次,利用ADN定理和迭代方法,证明了方程稳态强解的存在性.最后,利用ADN定理及Schauder估计,研究了方程稳态古典解的存在性.第二部分,利用T-弱连续算子方法,证明了热盐环流方程全局弱解的存在性.第三部分,研究了热盐环流方程弱吸引子的存在性.首先,利用Galerkin方法,得到了全局弱解满足的能量不等式.其次,根据能量不等式和多值半流理论,证明了在弱拓扑空间中存在吸引子.
[Abstract]:In this paper, we study the steady-state solution of the thermo-salt circulation equation and the existence of weak attractor, which consists of the following three parts. In the first part, we study the existence and regularity of the steady-state solution of the thermo-salt circulation equation. Firstly, the existence of steady-state weak solutions of thermo-salt circulation equations is studied by using the acute angle principle of weakly continuous operators. Secondly, the existence of steady-state strong solutions of the equation is proved by using ADN theorem and iterative method. Finally, by using ADN theorem and Schauder estimate, the existence of steady-state classical solutions of the equation is studied. In the second part, the existence of the global weak solution of the thermohaline circulation equation is proved by using the T- weakly continuous operator method. In the third part, we study the existence of weak attractor in the thermohaline circulation equation. Firstly, the energy inequality of global weak solution is obtained by using Galerkin method. Secondly, according to energy inequality and multi-valued half-flow theory, the existence of attractors in weak topological spaces is proved.
【学位授予单位】：四川师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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