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| 一类流体动力方程周期解的存在性和唯一性 | |
| 引用本文： | 金珍,万龙.一类流体动力方程周期解的存在性和唯一性[J].浙江大学学报(理学版),2017,44(1):40-46. |
| 作者姓名： | 金珍 万龙 |
| 作者单位： | 1. 南昌工程学院 理学院, 江西 南昌 330099; 2. 江西财经大学 信息管理学院, 江西 南昌 330013 |
| 基金项目： | 江西省教育厅科技项目（GJJ150463.GJJ150464）；江西省自然科学基金资助项目（20151BAB211009，20161BAB201028）；国家自然科学青年基金项目（11601198）；南昌工程学院青年基金项目（2014KJ024） |
| 摘 要： | 研究了一类非齐次流体动力方程的周期解的存在性和唯一性.首先采用Galerkin方法构造近似时间周期解序列,然后利用先验估计和Leray-Schauder不动点定理,证明近似时间周期解序列的收敛性,从而得到了该问题时间周期解的存在性,并且证明在一定条件下该解的唯一性. |
| 关 键 词： | 流体动力方程 周期解 Galerkin方法 Leray-Schauder不动点定理 |
| 收稿时间： | 2015-01-19 |
Existence and uniqueness of time periodic solution for the fluid dynamics equation |
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| JIN Zhen,WAN Long.Existence and uniqueness of time periodic solution for the fluid dynamics equation[J].Journal of Zhejiang University(Sciences Edition),2017,44(1):40-46. | |
| Authors: | JIN Zhen WAN Long |
| Institution: | 1. College of Science, Nanchang Institute of Technology, Nanchang 330099, China; 2. School of Information Technology, Jiangxi University of Finance and Economics, Nanchang 330013, China |
| Abstract: | This paper studies the existence and uniqueness of time periodic solution for one type of fluid dynamics equation with inhomogeneous term. Firstly, the approximation sequence of time periodic solution is constructed using the Galerkin method. Next, the approximation sequence is verified to be convergent by means of a priori estimate and Leray-Schauder fixed point theorem. It is shown that there is a time periodic solution when the inhomogeneous term is periodic about time. We also prove that the solution is unique under certain conditions. |
| Keywords: | fluid dynamics equation periodic solution Galerkin method Leray-Schauder fixed point theorem |
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