On exact boundary zero-controllability of two-dimensional Navier-Stokes equations. (English) Zbl 0809.93006

Fursikov, A. V.; Imanuvilov, O. Yu.

Acta Appl. Math. 37, No. 1-2, 67-76 (1994).

Summary: For two-dimensional Navier-Stokes equations defined in a bounded domain \(\Omega\) and for an arbitrary initial vector field, we construct the boundary Dirichlet condition that is tangent to the boundary \(\partial\Omega\) of \(\Omega\) and satisfies the property: the solution \(v(t,x)\) of the mentioned boundary-value problem equals zero at a certain finite time moment \(T\). Moreover, \[ \| x(t,\cdot) \|_{L_ 2 (\Omega)}\leq c\exp \Biggl( {{-k} \over {(T-t)^ 2}} \Biggr) \qquad \text{as } t\to T, \] where \(c>0\), \(k>0\) constants.

MSC:

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

Keywords:

exact boundary zero-controllability; boundary control; two-dimensional Navier-Stokes equations; boundary Dirichlet condition

References:

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