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We investigate the null controllability property of systems thatmathematically describe the dynamics of some non-Newtonian incompressibleviscous flows. The principal model we study was proposed by O. A.Ladyzhenskaya, although the techniques we develop here apply to other fluidshaving a shear-dependent viscosity. Taking advantage of the Pontryagin MinimumPrinciple, we utilize a bootstrapping argument to prove that sufficientlysmooth controls to the forced linearized Stokes problem exist, as long as theinitial data in turn has enough regularity. From there, we extend the result tothe nonlinear problem. As a byproduct, we devise a quasi-Newton algorithm tocompute the states and a control, which we prove to converge in an appropriatesense. We finish the work with some numerical experiments.

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