Existence and uniqueness of time periodic solution for the fluid dynamics equation - Jin, Zhen; Wan, Long (Zhejiang da xue xue bao. Journal of Zhejiang University. Sciences edition. Li xue ban, 2017)
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.