Abstract
The problem of partial controllability for the Navier-Stokes equations of viscous incompressible fluid is considered. The problem is to create in a given moment of time a velocity field with the null projection on the finitedimensional subspace spanned by eigenfunctions of the Stokes operator. The control is selected from this subspace too. On the basis of estimates of the solution for the subdifferential Cauchy problem for a Navier—Stokes system, controllability of the flow is proven on the condition that the norm of the control is minimal.
This work was supported by the Russian Foundation for Basic Research, grant No. 06-01-96003.
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© 2009 Birkhäuser Verlag Basel/Switzerland
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Chebotarev, A.Y. (2009). Finite-dimensional Control for the Navier—Stokes Equations. In: Fursikov, A.V., Galdi, G.P., Pukhnachev, V.V. (eds) New Directions in Mathematical Fluid Mechanics. Advances in Mathematical Fluid Mechanics. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0152-8_6
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DOI: https://doi.org/10.1007/978-3-0346-0152-8_6
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