Flow invariance preserving feedback controllers for the Navier-Stokes equation

In this paper we develop a concrete procedure fur designing feedback contro llers to ensure that the resultant dynamics of turbulence will preserve cer tain prescribed physical constraints. Examples of such constraints include, in particular, the level sets of well known invariants of the inviscid how 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 Na vier-Stokes inclusion with a multi-valued feedback term. (C) 2001 Academic Press.