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@article{MM_2017_29_11_a6, author = {A. A. Kornev}, title = {Modeling the stabilization process on the boundary conditions for the quasi-two-dimensional fluid with the four vortex structure}, journal = {Matemati\v{c}eskoe modelirovanie}, pages = {99--110}, publisher = {mathdoc}, volume = {29}, number = {11}, year = {2017}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/MM_2017_29_11_a6/} }
TY - JOUR AU - A. A. Kornev TI - Modeling the stabilization process on the boundary conditions for the quasi-two-dimensional fluid with the four vortex structure JO - Matematičeskoe modelirovanie PY - 2017 SP - 99 EP - 110 VL - 29 IS - 11 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MM_2017_29_11_a6/ LA - ru ID - MM_2017_29_11_a6 ER -
%0 Journal Article %A A. A. Kornev %T Modeling the stabilization process on the boundary conditions for the quasi-two-dimensional fluid with the four vortex structure %J Matematičeskoe modelirovanie %D 2017 %P 99-110 %V 29 %N 11 %I mathdoc %U http://geodesic.mathdoc.fr/item/MM_2017_29_11_a6/ %G ru %F MM_2017_29_11_a6
A. A. Kornev. Modeling the stabilization process on the boundary conditions for the quasi-two-dimensional fluid with the four vortex structure. Matematičeskoe modelirovanie, Tome 29 (2017) no. 11, pp. 99-110. http://geodesic.mathdoc.fr/item/MM_2017_29_11_a6/
[1] E.Z. Gak, Magnintye polia i vodnye eloktrolity, «Elmor», Sankt-Peterbyrg, 2013, 535 pp.
[2] M.Z. Gak, “Laboratornoe issledovanie avtokolebanii v sisteme chetyrekh vikhrei”, Izv. AN SSSR. Fiz. Atmos. Okeana, 17:2 (1981), 201–205
[3] L.A. Pleshanova, “Avtokolebaniia v sisteme cheturekh vikhrei”, Izv. AN SSSR. Fiz. Atmos. Okeana, 18:4 (1982), 339–348
[4] A. Thess, “Instabilities in two-dimensional spatially periodic flows”, Phys. Fluids A, 4:7 (1992), 1396–1407 | DOI | MR | Zbl
[5] S.D. Danilov, V.A. Dovzhenko, “Dokriticheskoe techenie v sisteme chetyrekh vikhrei”, Izv. AN SSSR. Fiz. Atmos. Okeana, 31:5 (1995), 621–626
[6] S.D. Danilov, F.V. Dolzhanskii, V.A. Dovzhenko, V.A. Krymov, “An advanced investigation of interaction of allocated quasi-two-dimensional vortices”, CHAOS, 6:3 (1996), 297–308 | DOI
[7] A.V. Fursikov, A.A. Kornev, “Feedback stabilization for Navier-Stokes equations: Theory and Calculations”, Mathematical Aspects of Fluid Mechanics, Lecture notes series, Cambridge University Press, 2012, 130–172 | MR | Zbl
[8] A.M. Lyapunov, The General Problem of the Stability of Motion, Taylor Francis, London, 1992 | MR | Zbl
[9] E.V. Chizhonkov, “Numerical aspects of one stabilization method”, Russ. J. Numer. Anal. and Math. Modelling, 18:5 (2003), 363–376 | DOI | MR | Zbl
[10] A.A. Kornev, “On an Iterative Method for the Construction of Hadamard Mustaches”, Comput. Math. Math. Phys., 44 (2004), 1274–1283 | MR | Zbl
[11] A.A. Kornev, “Classification of Methods of Approximate Projection onto a Stable Manifold”, Dokl., 71 (2005), 124–126 | MR
[12] A.A. Kornev, “The method of asymptotic stabilization to a given trajectory based on a correction of the initial data”, Comput. Math. Math. Phys., 46:1 (2006), 34–48 | DOI | MR | Zbl
[13] A.A Ivanchikov, “On numerical stabilizations of unstable Couette flow by the boundary condition”, Russ. J. Numer. Anal. and Math. Modelling, 21:6 (2006), 519–537 | DOI | MR | Zbl
[14] A.A. Ivanchikov, A.A. Kornev, A.V. Ozeritskii, “On a new approach to asymptotic stabilization problems”, Comp. Math. and Math. Phys., 49:12 (2009), 2070–2084 | DOI | MR
[15] A.A. Kornev, “Numerical aspects of a problem asymptotic stabilization by the right-hand side”, Russ. J. Numer. Anal. and Math. Modelling, 23:4 (2008), 407–422 | DOI | MR | Zbl
[16] A.V. Fursikov, “Real Processes and Realizability of a Stabilization Method for Navier-Stokes Equations by Boundary Feedback Control”, Nonlinear Problems in Mathematical Physics and Related Topics II, In Honor of Professor O. A.Ladyzhenskaya, Kluwer/Plenum Publishers, New-York–Boston–Dordrecht–London–Moscow, 137–177 | MR | Zbl
[17] O.A. Ladyzhenskaya, V.A. Solonnikov, “O printsipe linearizatsii i invariantnyh mnogoobraziiah dlia zadach magnitnoi gidrodinamiki”, Zap. Nauchn. cem. LOMI, 38, 1973, 46–93 | Zbl
[18] D.V. Anosov, “A multidimentional analog of a theorem of Hadamard”, Nauchn. Dokl. Vyssh. Shkoly Fiz.-Mat. Nauki, 1959, no. 1, 3–12
[19] Ya.B. Pesin, “Characteristic Lyapunov Exponents and Smooth Ergodic Theory”, Usp. Mat. Nauk, 32:4(196) (1977), 55–112 | Zbl