一类流体动力方程周期解的存在性和唯一性

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

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.

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.