Resolution of the Navier-Stokes equations in vorticity-velocity formulation via control techniques

The velocity-vorticity formulation of the Navier-Stokes equations is turned into an optimal control problem subject to linear constraints which consist of Laplacian equations for the velocity and for the vorticity. Various optimization algorithms can be used for the numerical resolution of the optimal control problem in question; in particular, the use of a conjugate-gradient method is discussed.