Exact controllability of Galerkin’s approximations of micropolar fluids

Abstract

We consider the nonlinear model describing micropolar fluid in a bounded smooth region of R N ( N = 2 , 3 ) \mathbb {R}^{N} (N=2,3) with distributed controls supported in small subset of this domain. Under suitable assumptions on the Galerkin basis, we introduce Galerkin’s approximations for the controllable micropolar fluid system. By using the Hilbert Uniqueness Method in combination with a fixed point argument, we prove the exact controllability result for this finite-dimensional system.