Non-Newtonian fluids are characterized by a viscosity that takes memory effects into account, meaning that the equations describing their flow are similar to Euler or Navier-Stokes equations with the addition of a nonlinear term. In many cases, the resulting equations are quasilinear, and the nonlinearity takes the form of p-growth.

In this talk, we will see that this viscosity term can imply stopping fluid flow in a finite time, and then we will look at the controllability of quasilinear parabolic equations with such nonlinearities. More specifically, we will show how the finite stopping time property can influence the null controllability of solutions.

We conclude by presenting a model for which the finite stopping time property is non-trivial (or unavailable), highlighting prospects for further development.