Exact controllability in projections for three-dimensional Navier–Stokes equations

Armen Shirikyan

Annales de l'I.H.P. Analyse non linéaire (2007)

  • Volume: 24, Issue: 4, page 521-537
  • ISSN: 0294-1449

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Shirikyan, Armen. "Exact controllability in projections for three-dimensional Navier–Stokes equations." Annales de l'I.H.P. Analyse non linéaire 24.4 (2007): 521-537. <http://eudml.org/doc/78747>.

@article{Shirikyan2007,
author = {Shirikyan, Armen},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {exact controllability in projections; 3D Navier-Stokes equations; Agrachev-Sarychev equations; strong solution},
language = {eng},
number = {4},
pages = {521-537},
publisher = {Elsevier},
title = {Exact controllability in projections for three-dimensional Navier–Stokes equations},
url = {http://eudml.org/doc/78747},
volume = {24},
year = {2007},
}

TY - JOUR
AU - Shirikyan, Armen
TI - Exact controllability in projections for three-dimensional Navier–Stokes equations
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2007
PB - Elsevier
VL - 24
IS - 4
SP - 521
EP - 537
LA - eng
KW - exact controllability in projections; 3D Navier-Stokes equations; Agrachev-Sarychev equations; strong solution
UR - http://eudml.org/doc/78747
ER -

References

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  1. [1] Agrachev A.A., Sarychev A.V., Navier–Stokes equations: controllability by means of low modes forcing, J. Math. Fluid Mech.7 (2005) 108-152. Zbl1075.93014
  2. [2] A.A. Agrachev, A.V Sarychev, Controllability of 2D Euler and Navier–Stokes equations by degenerate forcing, Comm. Math. Phys. (2006), in press. Zbl1105.93008
  3. [3] Barbu V., Sritharan S.S., Flow invariance preserving feedback controllers for the Navier–Stokes equation, J. Math. Anal. Appl.255 (2001) 281-307. Zbl1073.93030
  4. [4] Barbu V., Triggiani R., Internal stabilization of Navier–Stokes equations with finite-dimensional controllers, Indiana Univ. Math. J.53 (2004) 1443-1494. Zbl1073.76017
  5. [5] Coron J.-M., On the controllability of the 2-D incompressible Navier–Stokes equations with the Navier slip boundary conditions, ESAIM Control Optim. Calc. Var.1 (1995/96) 35-75, (electronic). Zbl0872.93040
  6. [6] Coron J.-M., On the controllability of 2-D incompressible perfect fluids, J. Math. Pures Appl.75 (1996) 155-188. Zbl0848.76013MR1380673
  7. [7] Coron J.-M., Fursikov A.V., Global exact controllability of the 2D Navier–Stokes equations on a manifold without boundary, Russian J. Math. Phys.4 (1996) 429-448. Zbl0938.93030
  8. [8] Coron J.-M., On the null asymptotic stabilization of the two-dimensional incompressible Euler equations in a simply connected domain, SIAM J. Control Optim.37 (1999) 1874-1896, (electronic). Zbl0954.76010MR1720143
  9. [9] Fernández-Cara E., On the approximate and null controllability of the Navier–Stokes equations, SIAM Rev.41 (1999) 269-277, (electronic). Zbl0945.93017
  10. [10] Fursikov A.V., Exact boundary zero controllability of three-dimensional Navier–Stokes equations, J. Dynam. Control Systems1 (1995) 325-350. Zbl0951.93005
  11. [11] Fursikov A.V., Emanuilov O.Yu., Exact controllability of the Navier–Stokes and Boussinesq equations, Russian Math. Surveys54 (1999) 565-618. Zbl0970.35116
  12. [12] Fursikov A.V., Stabilizability of two-dimensional Navier–Stokes equations with help of a boundary feedback control, J. Math. Fluid Mech.3 (2001) 259-301. Zbl0983.93021
  13. [13] Fursikov A.V., Stabilization for the 3D Navier–Stokes system by feedback boundary control, Discrete Contin. Dynam. Syst.10 (2004) 289-314. Zbl1174.93675
  14. [14] Glass O., Exact boundary controllability of 3-D Euler equation, ESAIM Control Optim. Calc. Var.5 (2000) 1-44, (electronic). Zbl0940.93012MR1745685
  15. [15] Imanuvilov O.Yu., On exact controllability for the Navier–Stokes equations, ESAIM Control Optim. Calc. Var.3 (1998) 97-131, (electronic). Zbl1052.93502
  16. [16] A. Shirikyan, Approximate controllability of three-dimensional Navier–Stokes equations, Comm. Math. Phys. (2006), in press. Zbl1105.93016
  17. [17] Taylor M.E., Partial Differential Equations. I–III, Springer-Verlag, New York, 1996. Zbl0869.35003
  18. [18] Temam R., Navier–Stokes Equations, North-Holland, Amsterdam, 1979. Zbl0426.35003

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