Existence and uniqueness of time periodic solution for the fluid dynamics equation

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 conver...

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Published inZhejiang da xue xue bao. Journal of Zhejiang University. Sciences edition. Li xue ban Vol. 44; no. 1; pp. 40 - 46
Main Authors Jin, Zhen, Wan, Long
Format Journal Article
LanguageChinese
Published Zhejiang University Press 01.01.2017
Subjects
Approximation
Estimates
Fixed points (mathematics)
Fluid dynamics
Galerkin methods
galerkin方法
leray-schauder不动点定理
Mathematical analysis
Theorems
Uniqueness
周期解
流体动力方程
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ISSN1008-9497
DOI10.3785/j.issn.1008-9497.2017.01.006

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Summary: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.
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ISSN:1008-9497
DOI:10.3785/j.issn.1008-9497.2017.01.006