Abstract
This paper deals with the boundary controllability of inviscid incompressible fluids for which thermal effects are important. They will be modeled through the so-called Boussinesq approximation. In the zero heat diffusion case, by adapting and extending some ideas from J.-M. Coron and O. Glass, we establish the simultaneous global exact controllability of the velocity field and the temperature for 2D and 3D flows. When the heat diffusion coefficient is positive, we present some additional results concerning exact controllability for the velocity field and local null controllability of the temperature.
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The authors are grateful to the anonymous referees for their valuable comments and suggestions that have allowed to improve a previous version of the paper.
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E. Fernández-Cara was partially supported by Grant MTM2010-15592 (DGI-MICINN, Spain). M. C. Santos was partially supported by CAPES. D. A. Souza was partially supported by CAPES (Brazil) and Grant MTM2010-15592 (DGI-MICINN, Spain).
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Fernández-Cara, E., Santos, M.C. & Souza, D.A. Boundary controllability of incompressible Euler fluids with Boussinesq heat effects. Math. Control Signals Syst. 28, 7 (2016). https://doi.org/10.1007/s00498-015-0158-x
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DOI: https://doi.org/10.1007/s00498-015-0158-x