Flow Invariance Preserving Feedback Controllers for the Navier–Stokes Equation

In this paper we develop a concrete procedure for designing feedback controllers to ensure that the resultant dynamics of turbulence will preserve certain prescribed physical constraints. Examples of such constraints include, in particular, the level sets of well known invariants of the inviscid flow such as helicity. We also bring to light a certain m-accretivity property of suitable quantization of the nonlinearity in the Navier–Stokes equation and utilize the theory of nonlinear semigroups to resolve the controlled Navier–Stokes inclusion with a multi-valued feedback term.