Exact boundary controllability of 3-D Euler equation

Olivier Glass

ESAIM: Control, Optimisation and Calculus of Variations (2000)

  • Volume: 5, page 1-44
  • ISSN: 1292-8119

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Glass, Olivier. "Exact boundary controllability of 3-D Euler equation." ESAIM: Control, Optimisation and Calculus of Variations 5 (2000): 1-44. <http://eudml.org/doc/90567>.

@article{Glass2000,
author = {Glass, Olivier},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {boundary controllability; exact controllability; control of fluid flow; 3-D Euler equation},
language = {eng},
pages = {1-44},
publisher = {EDP Sciences},
title = {Exact boundary controllability of 3-D Euler equation},
url = {http://eudml.org/doc/90567},
volume = {5},
year = {2000},
}

TY - JOUR
AU - Glass, Olivier
TI - Exact boundary controllability of 3-D Euler equation
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2000
PB - EDP Sciences
VL - 5
SP - 1
EP - 44
LA - eng
KW - boundary controllability; exact controllability; control of fluid flow; 3-D Euler equation
UR - http://eudml.org/doc/90567
ER -

References

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  1. [1] C. Bardos and U. Frisch, Finite-time regularity for bounded and unbounded ideal incompressible fluids using Hölder estimates, in Proceedings of the conference held at the university of Paris-Sud Orsay, France. Springer-Verlag, Lectures Notes in Math. 565 ( 1975) 1-13. Zbl0355.76016MR467034
  2. [2] J.-M. Coron, Global Asymptotic Stabilization for controllable systems without drift. Math. Control Signals Systems 5 ( 1992) 295-312. Zbl0760.93067MR1164379
  3. [3] J.-M. Coron, Contrôlabilité exacte frontière de l'équation d'Euler des fluides parfaits incompressibles bidimensionnels. C. R. Acad. Sci. Paris Sér. I Math. 317 ( 1993) 271-276. Zbl0781.76013MR1233425
  4. [4] J.-M. Coron, On the controllability of 2-D incompressible perfect fluids. J. Math. Pures Appl. 75 ( 1996) 155-188. Zbl0848.76013MR1380673
  5. [5] J.-M. Coron, On the controllability of the 2-D incompressible Navier-Stokes equations with the Navier slip boundary conditions. ESAIM Control Optim. Calc. Var. 1 ( 1996) 35-75. http://www.emath.fr/cocv/. Zbl0872.93040MR1393067
  6. [6] O. Glass, Exact boundary controllability of 3-D Euler equation of perfect incompressible fluids. C. R. Acad. Sci. Paris Sér. I Math. 325 ( 1997) 987-992. Zbl0897.76014MR1485616
  7. [7] O. Glass, Contrôlabilité de l'équation d'Euler tridimensionnelle pour les fluides parfaits incompressibles, Séminaire Équations aux Dérivées Partielles, 1997-1998, École polytechnique, Centre de Mathématiques, exposé XV. Zbl1175.93030MR1660528
  8. [8] P. Hermann and H. Kersten, Über die stetige Abhängigkeit der Lösung des Neumann-Problems für die Prae-Maxwellschen Gleichungen von ihren Randdaten. Arch. Math. (Basel) 36 ( 1981) 79-82. Zbl0449.35031MR612240
  9. [9] A.V. Kazhikov, Note on the formulation of the problem of flow through a bounded region using equations of perfect fluid. PMM USSR 44 ( 1981) 672-674. Zbl0468.76004
  10. [10] J.-L. Lions, Are there connections between turbulence and controllability?, 9th INRIA International Conference, Antibes (June 12-15, 1990). 
  11. [11] R. Temam, Navier-Stokes equations and numerical analysis. North-Holland Pub. ( 1979). Zbl0426.35003MR603444

Citations in EuDML Documents

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  1. Hayk Nersisyan, Controllability of 3D incompressible Euler equations by a finite-dimensional external force
  2. Rodrigo Lecaros, Lionel Rosier, Control of underwater vehicles in inviscid fluids
  3. Olivier Glass, Existence of solutions for the two-dimensional stationary Euler system for ideal fluids with arbitrary force
  4. S. Guerrero, O. Yu. Imanuvilov, Remarks on global controllability for the Burgers equation with two control forces
  5. Armen Shirikyan, Exact controllability in projections for three-dimensional Navier–Stokes equations
  6. Jaime H. Ortega, Lionel Rosier, Takéo Takahashi, Classical solutions for the equations modelling the motion of a ball in a bidimensional incompressible perfect fluid
  7. Olivier Glass, A controllability result for the 1 -D isentropic Euler equation
  8. Karine Beauchard, Controllability of Schrödinger equations
  9. Sylvain Ervedoza, Local exact controllability for the 1 -d compressible Navier-Stokes equations
  10. Jaime H. Ortega, Lionel Rosier, Takéo Takahashi, Classical solutions for the equations modelling the motion of a ball in a bidimensional incompressible perfect fluid

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