熱鹽環(huán)流方程的漸近理論
發(fā)布時間：2018-08-25 10:50
【摘要】：本文研究了熱鹽環(huán)流方程穩(wěn)態(tài)解以及弱吸引子的存在性,包含以下三個部分.第一部分,研究了熱鹽環(huán)流方程穩(wěn)態(tài)解的存在性與正則性.首先,利用弱連續(xù)算子的銳角原理,研究了熱鹽環(huán)流方程穩(wěn)態(tài)弱解的存在性.其次,利用ADN定理和迭代方法,證明了方程穩(wěn)態(tài)強(qiáng)解的存在性.最后,利用ADN定理及Schauder估計(jì),研究了方程穩(wěn)態(tài)古典解的存在性.第二部分,利用T-弱連續(xù)算子方法,證明了熱鹽環(huán)流方程全局弱解的存在性.第三部分,研究了熱鹽環(huán)流方程弱吸引子的存在性.首先,利用Galerkin方法,得到了全局弱解滿足的能量不等式.其次,根據(jù)能量不等式和多值半流理論,證明了在弱拓?fù)淇臻g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.
【學(xué)位授予單位】：四川師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175
本文編號：2202657
[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.
【學(xué)位授予單位】：四川師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175
【參考文獻(xiàn)】
相關(guān)期刊論文 前2條
1 房少梅;金玲玉;郭柏靈;;Existence of weak solution for quantum Zakharov equations for plasmas model[J];Applied Mathematics and Mechanics(English Edition);2011年10期
2 顧永耕,孫文俊;NONTRIVIAL EQUILIBRIUM SOLUTIONS FOR A SEMILINEAR REACTION-DIFFUSION SYSTEM[J];Applied Mathematics and Mechanics(English Edition);2004年12期
，本文編號：2202657
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