Insensitizing controls for the micropolar fluids

Abstract

In this paper, we investigate the existence of insensitizing controls for the micropolar fluids in a bounded domain with homogeneous Dirichlet boundary conditions and arbitrarily located internal controller. The study of insensitizing controls is essential to solve a stability problem, which means that we look for controls such that some functionals of the velocity fields (the so‐called sentinels) are insensitive to the small perturbations of initial data. The problem of insensitizing controls is transformed into a suitable controllability problem for a cascade system. Our proof relies on a new global Carleman inequality and the inverse mapping theorem.