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Sylvain Ervedoza
Local exact controllability for the $1$-d compressible Navier-Stokes equations
Séminaire Laurent Schwartz — EDP et applications (2011-2012), Exp. No. 39, 14 p., doi: 10.5802/slsedp.30
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Résumé - Abstract

In this talk, I will present a recent result obtained in [6] with O. Glass, S. Guerrero and J.-P. Puel on the local exact controllability of the $1$-d compressible Navier-Stokes equations. The goal of these notes is to give an informal presentation of this article and we refer the reader to it for extensive details.


[1] E.V. Amosova. Exact local controllability for the equations of viscous gas dynamics. Differentsial’nye Uravneniya, 47(12):1754–1772, 2011.  MR 2963212 |  Zbl 1241.93006
[2] S. Chowdhury, M. Ramaswamy, and J.-P. Raymond. Controllability and stabilizability of the linearized compressible Navier-Stokes in one dimension. Submitted, 2012.
[3] J.-M. Coron. On the controllability of $2$-D incompressible perfect fluids. J. Math. Pures Appl. (9), 75(2):155–188, 1996.  MR 1380673 |  Zbl 0848.76013
[4] J.-M. Coron. Control and nonlinearity, volume 136 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2007.  MR 2302744 |  Zbl 1140.93002
[5] J.-M. Coron and A. V. Fursikov. Global exact controllability of the $2$D Navier-Stokes equations on a manifold without boundary. Russian J. Math. Phys., 4(4):429–448, 1996.  MR 1470445 |  Zbl 0938.93030
[6] S. Ervedoza, O. Glass, S. Guerrero, and J.-P. Puel. Local exact controllability for the $1$-D compressible Navier Stokes equation. Arch. Ration. Mech. Anal., to appear.  MR 2968594
[7] E. Fernández-Cara, S. Guerrero, O. Yu. Imanuvilov, and J.-P. Puel. Local exact controllability of the Navier-Stokes system. J. Math. Pures Appl. (9), 83(12):1501–1542, 2004.  MR 2103189 |  Zbl pre02164954
[8] A. V. Fursikov and O. Y. Imanuvilov. Controllability of evolution equations, volume 34 of Lecture Notes Series. Seoul National University Research Institute of Mathematics Global Analysis Research Center, Seoul, 1996.  MR 1406566 |  Zbl 0862.49004
[9] O. Glass. Exact boundary controllability of 3-D Euler equation. ESAIM Control Optim. Calc. Var., 5:1–44 (electronic), 2000. Numdam |  MR 1745685 |  Zbl 0940.93012
[10] O. Glass. On the controllability of the 1-D isentropic Euler equation. J. Eur. Math. Soc. (JEMS), 9(3):427–486, 2007.  MR 2314104 |  Zbl 1139.35014
[11] M. González-Burgos, S. Guerrero, and J.-P. Puel. Local exact controllability to the trajectories of the Boussinesq system via a fictitious control on the divergence equation. Commun. Pure Appl. Anal., 8(1):311–333, 2009.  MR 2449112 |  Zbl 1152.93005
[12] S. Guerrero and O. Y. Imanuvilov. Remarks on global controllability for the Burgers equation with two control forces. Ann. Inst. H. Poincaré Anal. Non Linéaire, 24(6):897–906, 2007.  MR 2371111 |  Zbl 1248.93024
[13] O. Y. Imanuvilov. Remarks on exact controllability for the Navier-Stokes equations. ESAIM Control Optim. Calc. Var., 6:39–72 (electronic), 2001. Numdam |  MR 1804497 |  Zbl 0961.35104
[14] O. Y. Imanuvilov and J.-P. Puel. On global controllability of 2-D Burgers equation. Discrete Contin. Dyn. Syst., 23(1-2):299–313, 2009.  MR 2449080 |  Zbl 1158.93007
[15] T.-T. Li and B.-P. Rao. Exact boundary controllability for quasi-linear hyperbolic systems. SIAM J. Control Optim., 41(6):1748–1755 (electronic), 2003.  MR 1972532 |  Zbl 1032.35124
[16] P. Martin, L. Rosier, and P. Rouchon. Null-controllability of a structurally damped wave equation with moving point control. Submitted, 2012.
[17] A. Matsumura and T. Nishida. The initial value problem for the equations of motion of viscous and heat-conductive gases. J. Math. Kyoto Univ., 20(1):67–104, 1980.  MR 564670 |  Zbl 0429.76040
[18] H. Nersisyan. Controllability of the 3D compressible Euler system. Comm. Partial Differential Equations, 36(9):1544–1564, 2011.  MR 2825602 |  Zbl 1234.93016
[19] L. Rosier and P. Rouchon. On the controllability of a wave equation with structural damping. Int. J. Tomogr. Stat., 5(W07):79–84, 2007.  MR 2393756
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