On the control of a simplified k-e model of turbulence

This paper deals with the control of a kind of turbulent flows. We consider a simplified k-e model with distributed controls, locally supported in space. We proof that the system is partially locally null-controllable, in the sense that the velocity field can be driven exactly to zero if the initial state is small enough. The proof relies on an argument where we have concatenated several techniques: fixed-point formulation, linearization, energy and Carleman estimates, local inversion, etc. Ths result can be viewed as a nontrivial step towards the control of turbulent fluids.