Far Eastern Mathematical Journal

To content of the issue


Stabilization from the boundary of solution for Navier-Stokes system: solvability and justification of numerical simulation


A. V. Fursikov

2003, issue 1, P. 86–100


Abstract
A stabilization method for solution of Navier-Stokes system near steady-state (unstable) solution is expounded. Stabilization is done by a control from the boundary of the domain where equations are defined. Important point of the stabilization problem which we study in this paper is justification of possibility for numerical simulation. We solve the problem choosing feedback control.

Keywords:

Download the article (PDF-file)

References

[1] A. V. Fursikov, Stabiliziruemost' kvazilinejnogo parabolicheskogo uravneniya s pomoshh'yu granichnogo upravleniya s obratnoj svyaz'yu, Mat. sb., 192:4 (2001), 115–160.
[2] A. V. Fursikov, Stabilizability of two-dimensional Navier – Stokes equation with help of boundary feedback control, J. Math. Fluid Mech., 3 (2001), 259–301.
[3] A.V. Fursikov, Feedback stabilization for 2D Navier – Stokes equation, The Navier – Stokes equation: Theory and Numerical Methods, Lecture Note Pure Appl. Math., 223, 2001, 179–196.
[4] A. V. Fursikov, Feedback stabilization for 2D Ozeen equation: additienal remarks, Control and Estimation of Distributed Parameter Systems, International series of Numerical Mathematics, Burkha?ser Verlag, 2002, 169–188.
[5] A. V. Fursikov, Stabilization for the 3D Navier – Stikes system by feedback boundary control, Discrete Cont. Dyn. Syst., 9:6 (2003).
[6] A. V. Fursikov, Real process corresponding to 3D Navier – Stokes system and its feedback stabilization from boundary, Advances in the Math Sciences-51, PDE M. Vishik's Seminar, Amer. Math. Soc. Transl. Series 2, 206, AMS, Providence, Rhode Island, 2002, 95–123.
[7] A. V. Fursikov, Real'nye processy i realizuemost' metoda stabilizacii sistemy Nav'e – Stoksa posredstvom upravleniya s obratnoj svyaz'yu s granicy oblasti, Nelinejnye zadachi matematicheskoj fiziki i smezhnye voprosy. II, V chest' akademika O. A. Ladyzhenskoj, Mezhdunar. matem. seriya, 2, 2002, 127–164.
[8] M. V. Keldysh, O polnote sobstvennyx funkcij nekotoryx klassov nesamosopryazhennyx operatorov, UMN, 26:4 (1971), 15–41.
[9] O. A. Ladyzhenskaya, Matematicheskie voprosy dinamiki vyazkoj neszhimaemoj zhidkosti, Nauka, M., 1970.
[10] M. I. Vishik, A. V. Fursikov, Matematicheskie zadachi statisticheskoj gidromexaniki, Nauka, M., 1980.
[11] A. V. Babin, M. I. Vishik, Attraktory e'volyucionnyx uravnenij, Nauka, M., 1989.

To content of the issue