Global exact controllability of the 2D Navier-Stokes equations on a manifold without boundary. (English) Zbl 0938.93030

Coron, Jean-Michel; Fursikov, Andrei V.

Russ. J. Math. Phys. 4, No. 4, 429-448 (1996).

The main result is on global exact controllability of the Navier-Stokes equations in a two-dimensional connected compact Riemannian manifold without boundary; the control is applied on an arbitrary nonempty open subset of the surface. The proof combines global approximate controllability with local exact controllability.
The authors point out a possible application to climate control theory, where the manifold is the surface of a sphere.

Reviewer: H.O.Fattorini (Los Angeles)

MSC:

93C20	Control/observation systems governed by partial differential equations
93B05	Controllability
35Q30	Navier-Stokes equations
76D05	Navier-Stokes equations for incompressible viscous fluids

Keywords:

exact controllability; control of fluid flow; Navier-Stokes equations