Local null controllability of a class of non-Newtonian incompressible viscous fluids

<p style='text-indent:20px;'>We investigate the null controllability property of systems that mathematically describe dynamics some non-Newtonian incompressible viscous flows. The principal model we study was proposed by O. A. Ladyzhenskaya, although techniques develop here apply to other fluids having a shear-dependent viscosity. Taking advantage Pontryagin Minimum Principle, utilize bootstrapping argument prove sufficiently smooth controls forced linearized Stokes problem exist, as long initial data in turn has enough regularity. From there, extend result nonlinear problem. As byproduct, devise quasi-Newton algorithm compute states and control, which converge an appropriate sense. We finish work with numerical experiments.</p>