On exact boundary zero-controlability of two-dimensional Navier-Stokes equations |
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Authors: | A V Fursikov O Yu Imanuvilov |
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Institution: | 1. Department of Mechanics and Mathematics, Moscow State University, 119899, Moscow, Russia 2. Department of Applied Mathematics, Moscow State University of the Forest, Mytischi-1, 141000, Moscow Region, Russia
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Abstract: | For two-dimensional Navier-Stokes equations defined in a bounded domain Ω and for an arbitrary initial vector field, we construct the boundary Dirichlet condition that is tangent to the boundary ?Ω of Ω and satisfies the property: the solutionυ(t, x) of the mentioned boundary-value problem equals zero at a certain finite time momentT. Moreover, $$\parallel x(t, \cdot )\parallel _{L_2 (\Omega )} \leqslant c\exp \left( {\tfrac{{ - k}}{{(T - t)^2 }}} \right)ast \to T,$$ wherec > 0,k > 0 constants. |
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