American Institute of Mathematical Sciences

December  2012, 2(4): 361-382. doi: 10.3934/mcrf.2012.2.361

Local controllability of the $N$-dimensional Boussinesq system with $N-1$ scalar controls in an arbitrary control domain

 1 Université Pierre et Marie Curie, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France

Received  March 2012 Revised  April 2012 Published  October 2012

In this paper we deal with the local exact controllability to a particular class of trajectories of the $N$-dimensional Boussinesq system with internal controls having $2$ vanishing components. The main novelty of this work is that no condition is imposed on the control domain.
Citation: Nicolás Carreño. Local controllability of the $N$-dimensional Boussinesq system with $N-1$ scalar controls in an arbitrary control domain. Mathematical Control & Related Fields, 2012, 2 (4) : 361-382. doi: 10.3934/mcrf.2012.2.361
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References:
 [1] Belhassen Dehman, Jean-Pierre Raymond. Exact controllability for the Lamé system. Mathematical Control & Related Fields, 2015, 5 (4) : 743-760. doi: 10.3934/mcrf.2015.5.743 [2] Vena Pearl Bongolan-walsh, David Cheban, Jinqiao Duan. Recurrent motions in the nonautonomous Navier-Stokes system. Discrete & Continuous Dynamical Systems - B, 2003, 3 (2) : 255-262. doi: 10.3934/dcdsb.2003.3.255 [3] Mehdi Badra. Abstract settings for stabilization of nonlinear parabolic system with a Riccati-based strategy. Application to Navier-Stokes and Boussinesq equations with Neumann or Dirichlet control. Discrete & Continuous Dynamical Systems - A, 2012, 32 (4) : 1169-1208. doi: 10.3934/dcds.2012.32.1169 [4] Viorel Barbu, Ionuţ Munteanu. Internal stabilization of Navier-Stokes equation with exact controllability on spaces with finite codimension. Evolution Equations & Control Theory, 2012, 1 (1) : 1-16. doi: 10.3934/eect.2012.1.1 [5] Hammadi Abidi, Taoufik Hmidi, Sahbi Keraani. On the global regularity of axisymmetric Navier-Stokes-Boussinesq system. Discrete & Continuous Dynamical Systems - A, 2011, 29 (3) : 737-756. doi: 10.3934/dcds.2011.29.737 [6] Manuel González-Burgos, Sergio Guerrero, Jean Pierre Puel. Local exact controllability to the trajectories of the Boussinesq system via a fictitious control on the divergence equation. Communications on Pure & Applied Analysis, 2009, 8 (1) : 311-333. doi: 10.3934/cpaa.2009.8.311 [7] Mohammed Aassila. Exact boundary controllability of a coupled system. Discrete & Continuous Dynamical Systems - A, 2000, 6 (3) : 665-672. doi: 10.3934/dcds.2000.6.665 [8] Grzegorz Karch, Xiaoxin Zheng. Time-dependent singularities in the Navier-Stokes system. Discrete & Continuous Dynamical Systems - A, 2015, 35 (7) : 3039-3057. doi: 10.3934/dcds.2015.35.3039 [9] Igor Kukavica. Interior gradient bounds for the 2D Navier-Stokes system. Discrete & Continuous Dynamical Systems - A, 2001, 7 (4) : 873-882. doi: 10.3934/dcds.2001.7.873 [10] Atanas Stefanov. On the Lipschitzness of the solution map for the 2 D Navier-Stokes system. Discrete & Continuous Dynamical Systems - A, 2010, 26 (4) : 1471-1490. doi: 10.3934/dcds.2010.26.1471 [11] Mehdi Badra. Global Carleman inequalities for Stokes and penalized Stokes equations. Mathematical Control & Related Fields, 2011, 1 (2) : 149-175. doi: 10.3934/mcrf.2011.1.149 [12] Stanislaw Migórski, Anna Ochal. Navier-Stokes problems modeled by evolution hemivariational inequalities. Conference Publications, 2007, 2007 (Special) : 731-740. doi: 10.3934/proc.2007.2007.731 [13] A. V. Fursikov. Stabilization for the 3D Navier-Stokes system by feedback boundary control. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 289-314. doi: 10.3934/dcds.2004.10.289 [14] Yinghua Li, Shijin Ding, Mingxia Huang. Blow-up criterion for an incompressible Navier-Stokes/Allen-Cahn system with different densities. Discrete & Continuous Dynamical Systems - B, 2016, 21 (5) : 1507-1523. doi: 10.3934/dcdsb.2016009 [15] Pedro Marín-Rubio, Antonio M. Márquez-Durán, José Real. Three dimensional system of globally modified Navier-Stokes equations with infinite delays. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 655-673. doi: 10.3934/dcdsb.2010.14.655 [16] Kuanysh A. Bekmaganbetov, Gregory A. Chechkin, Vladimir V. Chepyzhov, Andrey Yu. Goritsky. Homogenization of trajectory attractors of 3D Navier-Stokes system with randomly oscillating force. Discrete & Continuous Dynamical Systems - A, 2017, 37 (5) : 2375-2393. doi: 10.3934/dcds.2017103 [17] Donatella Donatelli, Eduard Feireisl, Antonín Novotný. On incompressible limits for the Navier-Stokes system on unbounded domains under slip boundary conditions. Discrete & Continuous Dynamical Systems - B, 2010, 13 (4) : 783-798. doi: 10.3934/dcdsb.2010.13.783 [18] Lucas C. F. Ferreira, Elder J. Villamizar-Roa. On the existence of solutions for the Navier-Stokes system in a sum of weak-$L^{p}$ spaces. Discrete & Continuous Dynamical Systems - A, 2010, 27 (1) : 171-183. doi: 10.3934/dcds.2010.27.171 [19] Debanjana Mitra, Mythily Ramaswamy, Jean-Pierre Raymond. Largest space for the stabilizability of the linearized compressible Navier-Stokes system in one dimension. Mathematical Control & Related Fields, 2015, 5 (2) : 259-290. doi: 10.3934/mcrf.2015.5.259 [20] Reinhard Farwig, Paul Felix Riechwald. Regularity criteria for weak solutions of the Navier-Stokes system in general unbounded domains. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 157-172. doi: 10.3934/dcdss.2016.9.157

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