Local null controllability of the three-dimensional Navier-Stokes system with a distributed control having two vanishing components. (English) Zbl 1308.35163
This is a great paper showing the local null controllability of the Navier-Stokes system on a bounded domain \(\Omega \) of \({\mathbb{R}}^3\) with null Dirichlet boundary conditions. Specifically, the control is distributed in an arbitrary nonempty open subset of \(\Omega \) and has two vanishing components. While the linearized (around zero) system is not necessarily null controllable, even if the control is distributed in the entire \(\Omega \) (as proved by J.-L. Lions and E. Zuazua [Lect. Notes Pure Appl. Math. 177, 221–235 (1996; Zbl 0852.35112)]), the authors choose to linearize the system around a specific nonzero particular solution and show that the corresponding linearized system is null controllable. This allows them to show that the original system is locally null controllable by using an inverse mapping argument.
Reviewer: Gheorghe Moroşanu (Budapest)
Citations:
Zbl 0852.35112References:
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