Open Access
Volume 25, 2019
Article Number 66
Number of page(s) 35
Published online 01 November 2019
  1. S.N. Antontsev, A.V. Kazhikhov and V.N. Monakhov, Boundary value problems in mechanics of nonhomogeneous fluids. Vol. 22 of Studies in Mathematics and its Applications. Translated from the Russian. North-Holland Publishing Co., Amsterdam (1990). [Google Scholar]
  2. J-P. Aubin, Un théorème de compacité. C. R. Acad. Sci. Paris 256 (1963) 5042–5044. [Google Scholar]
  3. M. Badra and T. Takahashi, Stabilization of parabolic nonlinear systems with finite dimensional feedback or dynamical controllers: application to the Navier-Stokes system. SIAM J. Control Optim. 49 (2011) 420–463. [CrossRef] [MathSciNet] [Google Scholar]
  4. M. Badra and T. Takahashi, On the Fattorini criterion for approximate controllability and stabilizability of parabolic systems. ESAIM: COCV 20 (2014) 924–956. [CrossRef] [EDP Sciences] [Google Scholar]
  5. M. Badra, S. Ervedoza and S. Guerrero, Local controllability to trajectories for non-homogeneous incompressible Navier-Stokes equations. Ann. Inst. Henri Poincaré Anal. Non Linéaire 33 (2016) 529–574. [CrossRef] [Google Scholar]
  6. H. Bahouri, J-Y. Chemin and R. Danchin, Fourier analysis and nonlinear partial differential equations. Vol. 343 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer, Heidelberg (2011). [CrossRef] [Google Scholar]
  7. V. Barbu, Stabilization of a plane channel flow by wall normal controllers. Nonlinear Anal. 67 (2007) 2573–2588. [CrossRef] [Google Scholar]
  8. A. Bensoussan, G. Da Prato, M.C. Delfour and S.K. Mitter, Representation and control of infinite dimensional systems. Systems & Control: Foundations & Applications. Birkhäuser Boston, Inc., Boston, MA, second edition (2007). [CrossRef] [Google Scholar]
  9. F. Boyer, Trace theorems and spatial continuity properties for the solutions of the transport equation. Differ. Int. Equ. 18 (2005) 891–934. [Google Scholar]
  10. F. Boyer and P. Fabrie, Outflow boundary conditions for the incompressible non-homogeneous Navier-Stokes equations. Discrete Contin. Dyn. Syst. Ser. B 7 (2007) 219–250. [Google Scholar]
  11. F. Boyer and P. Fabrie, Mathematical tools for the study of the incompressible Navier-Stokes equations and related models. Vol. 183 of Applied Mathematical Sciences. Springer, New York (2013). [CrossRef] [Google Scholar]
  12. S. Chowdhury and S. Ervedoza, Open loop stabilization of incompressible Navier–Stokes equations in a 2d channel using power series expansion. J. Math. Pures Appl. 130 (2019) 301–346. [Google Scholar]
  13. S. Chowdhury, M. Ramaswamy and J.-P. Raymond, Controllability and stabilizability of the linearized compressible Navier-Stokes system in one dimension. SIAM J. Control Optim. 50 (2012) 2959–2987. [CrossRef] [MathSciNet] [Google Scholar]
  14. S. Chowdhury, D. Maity, M. Ramaswamy and J-P. Raymond, Local stabilization of the compressible Navier-Stokes system, around null velocity, in one dimension. J. Differ. Equ. 259 (2015) 371–407. [Google Scholar]
  15. J.M. Coron and P. Lissy, Local null controllability of the three-dimensional Navier-Stokes system with a distributed control having two vanishing components. Invent. Math. 198 (2014) 833–880. [Google Scholar]
  16. B. Desjardins, Linear transport equations with initial values in Sobolev spaces and application to the Navier-Stokes equations. Differ. Int. Equ. 10 (1997) 577–586. [Google Scholar]
  17. P. Deuring and W. von Wahl Strong solutions of the Navier-Stokes system in Lipschitz bounded domains. Math. Nachr. 171 (1995) 111–148. [CrossRef] [Google Scholar]
  18. R.J. DiPerna and P.-L. Lions, Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. 98 (1989) 511–547. [Google Scholar]
  19. S. Ervedoza, O. Glass and S. Guerrero, Local exact controllability for the two- and three-dimensional compressible Navier-Stokes equations. Comm. Partial Differ. Equ. 41 (2016) 1660–1691. [CrossRef] [Google Scholar]
  20. S. Ervedoza, O. Glass, S. Guerrero and J.-P Puel, Local exact controllability for the one-dimensional compressible Navier-Stokes equation. Arch. Ration. Mech. Anal. 206 (2012) 189–238. [Google Scholar]
  21. C. Fabreand G. Lebeau, Prolongement unique des solutions de l’equation de Stokes. Comm. Part. Differ. Equ. 21 (1996) 573–596. [CrossRef] [MathSciNet] [Google Scholar]
  22. A.V. Fursikov, Stabilizability of a quasilinear parabolic equation by means of boundary feedback control. Mat. Sb. [Google Scholar]
  23. A.V. Fursikov, Stabilizability of two-dimensional Navier-Stokes equations with help of a boundary feedback control. J. Math. Fluid Mech. 3 (2001) 259–301. [CrossRef] [MathSciNet] [Google Scholar]
  24. A.V. Fursikov, Stabilization for the 3D Navier-Stokes system by feedback boundary control. Discrete Contin. Dyn. Syst., 10 (2004) 289–314. [CrossRef] [MathSciNet] [Google Scholar]
  25. G.P. Galdi, An introduction to the mathematical theory of the Navier-Stokes equations. Vol. II. Vol. 39 of Springer Tracts in Natural Philosophy. Springer-Verlag, New York (1994). [Google Scholar]
  26. R.B. Kellogg and J.E. Osborn, A regularity result for the Stokes problem in a convex polygon. J. Funct. Anal. 21 (1976) 397–431. [Google Scholar]
  27. O.A. Ladyzhenskaya and V.A. Solonnikov, Unique solvability of an initial-and boundary-value problem for viscous incompressible nonhomogeneous fluids. J. Math. Sci. 9 (1978) 697–749. [CrossRef] [Google Scholar]
  28. G. Lebeau and E. Zuazua, Null-controllability of a system of linear thermoelasticity. Arch. Ration. Mech. Anal. 141 (1998) 297–329. [Google Scholar]
  29. J.-L. Lions and E. Magenes, Vol. I of Non-homogeneous boundary value problems and applications. Translated from the French by P. Kenneth, Die Grundlehren der mathematischen Wissenschaften, Band 181. Springer-Verlag, New York-Heidelberg (1972). [Google Scholar]
  30. V. Maz’ya and J. Rossmann, Elliptic equations in polyhedral domains. Vol. 162 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI (2010). [CrossRef] [Google Scholar]
  31. I. Munteanu, Normal feedback stabilization of periodic flows in a two-dimensional channel. J. Optim. Theory Appl. 152 (2012) 413–438. [Google Scholar]
  32. P.A. Nguyen and J.P. Raymond, Boundary stabilization of the Navier-Stokes equations in the case of mixed boundary conditions. SIAM J. Control Optim. 53 (2015) 3006–3039. [CrossRef] [Google Scholar]
  33. J.P. Raymond, Feedback boundary stabilization of the two-dimensional Navier-Stokes equations. SIAM J. Control Optim. 45 (2006) 790–828. [CrossRef] [MathSciNet] [Google Scholar]
  34. J.P. Raymond, Feedback boundary stabilization of the three-dimensional incompressible Navier-Stokes equations. J. Math. Pures Appl., 87 (2007) 627–669. [Google Scholar]
  35. J.P. Raymond, Stokes and Navier-Stokes equations with nonhomogeneous boundary conditions. Ann. Inst. Henri Poincaré Anal. Non Linéaire 24 (2007) 921–951. [CrossRef] [MathSciNet] [Google Scholar]
  36. J.P. Raymond and L. Thevenet, Boundary feedback stabilization of the two dimensional Navier-Stokes equations with finite dimensional controllers. Disc. Contin. Dyn. Syst. 27 (2010) 1159–1187. [CrossRef] [MathSciNet] [Google Scholar]
  37. R. Temam, Navier-Stokes equations. Theory and numerical analysis, With an appendix by F. Thomasset. Vol. 2 of Studies in Mathematics and its Applications. North-Holland Publishing Co., Amsterdam-New York, revised edition (1979). [Google Scholar]
  38. R. Triggiani, Boundary feedback stabilizability of parabolic equations. Appl. Math. Optim. 6 (1980) 201–220. [Google Scholar]
  39. R. Vazquez and M. Krstic, A closed-form feedback controller for stabilization of the linearized 2-D Navier-Stokes Poiseuille system. IEEE Trans. Automat. Control 52 (2007) 2298–2312. [CrossRef] [Google Scholar]
  40. R. Vázquez, E. Trélat and J-M. Coron, Control for fast and stable laminar-to-high-Reynolds-numbers transfer in a 2D Navier-Stokes channel flow. Discrete Contin. Dyn. Syst. Ser. B 10 (2008) 925–956. [CrossRef] [Google Scholar]
  41. E. Zuazua, Log-Lipschitz regularity and uniqueness of the flow for a field in (Wlocn/p+1,p(ℝn))n. C. R. Math. Acad. Sci. Paris 335 (2002) 17–22. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.