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 -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.
@article{SLSEDP_2011-2012____A39_0,
author = {Ervedoza, Sylvain},
title = {Local exact controllability for the $1$-d compressible {Navier-Stokes} equations},
journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
note = {talk:39},
pages = {1--14},
publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2011-2012},
doi = {10.5802/slsedp.30},
language = {en},
url = {http://www.numdam.org/articles/10.5802/slsedp.30/}
}
TY - JOUR AU - Ervedoza, Sylvain TI - Local exact controllability for the $1$-d compressible Navier-Stokes equations JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:39 PY - 2011-2012 SP - 1 EP - 14 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://www.numdam.org/articles/10.5802/slsedp.30/ DO - 10.5802/slsedp.30 LA - en ID - SLSEDP_2011-2012____A39_0 ER -
%0 Journal Article %A Ervedoza, Sylvain %T Local exact controllability for the $1$-d compressible Navier-Stokes equations %J Séminaire Laurent Schwartz — EDP et applications %Z talk:39 %D 2011-2012 %P 1-14 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U http://www.numdam.org/articles/10.5802/slsedp.30/ %R 10.5802/slsedp.30 %G en %F SLSEDP_2011-2012____A39_0
Ervedoza, Sylvain. Local exact controllability for the $1$-d compressible Navier-Stokes equations. Séminaire Laurent Schwartz — EDP et applications (2011-2012), Exposé no. 39, 14 p. doi : 10.5802/slsedp.30. http://www.numdam.org/articles/10.5802/slsedp.30/
[1] E.V. Amosova. Exact local controllability for the equations of viscous gas dynamics. Differentsial’nye Uravneniya, 47(12):1754–1772, 2011. | MR | Zbl
[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 -D incompressible perfect fluids. J. Math. Pures Appl. (9), 75(2):155–188, 1996. | MR | Zbl
[4] J.-M. Coron. Control and nonlinearity, volume 136 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2007. | MR | Zbl
[5] J.-M. Coron and A. V. Fursikov. Global exact controllability of the D Navier-Stokes equations on a manifold without boundary. Russian J. Math. Phys., 4(4):429–448, 1996. | MR | Zbl
[6] S. Ervedoza, O. Glass, S. Guerrero, and J.-P. Puel. Local exact controllability for the -D compressible Navier Stokes equation. Arch. Ration. Mech. Anal., to appear. | MR
[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
[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 | Zbl
[9] O. Glass. Exact boundary controllability of 3-D Euler equation. ESAIM Control Optim. Calc. Var., 5:1–44 (electronic), 2000. | Numdam | MR | Zbl
[10] O. Glass. On the controllability of the 1-D isentropic Euler equation. J. Eur. Math. Soc. (JEMS), 9(3):427–486, 2007. | MR | Zbl
[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 | Zbl
[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. | Numdam | MR | Zbl
[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 | Zbl
[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 | Zbl
[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 | Zbl
[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 | Zbl
[18] H. Nersisyan. Controllability of the 3D compressible Euler system. Comm. Partial Differential Equations, 36(9):1544–1564, 2011. | MR | Zbl
[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
Cité par Sources :
