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

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.

MSC:

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