Exact Controllability of Galerkin's Approximations for the Oldroyd Fluid System

Abstract

In this paper we investigate the model of Oldroyd Fluid in a bounded smooth region of Rn (n = 2, 3) with control supported in a small subset of this domain. Under suitable assumptions on the Galerkin basis, we introduce Galerkin's approximations for the Oldroyd fluid system. Using the Hilbert Uniqueness Method in combination with the Schauder's fixed point, we prove the exact controllability for this finite-dimensional system.