Abstract:
We study the linear stability of a stationary flow of an incompressible viscoelastic polymeric fluid in a plane infinite channel in the case of periodic perturbations with respect to a variable related to the length of the channel.
Citation:
A. M. Blokhin, D. L. Tkachev, “Linear asymptotic instability of a stationary flow of a polymeric medium in a plane channel in the case of periodic perturbations”, Sib. Zh. Ind. Mat., 17:3 (2014), 13–25; J. Appl. Industr. Math., 8:4 (2014), 467–478
\Bibitem{BloTka14}
\by A.~M.~Blokhin, D.~L.~Tkachev
\paper Linear asymptotic instability of a~stationary flow of a~polymeric medium in a~plane channel in the case of periodic perturbations
\jour Sib. Zh. Ind. Mat.
\yr 2014
\vol 17
\issue 3
\pages 13--25
\mathnet{http://mi.mathnet.ru/sjim842}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3364402}
\transl
\jour J. Appl. Industr. Math.
\yr 2014
\vol 8
\issue 4
\pages 467--478
\crossref{https://doi.org/10.1134/S1990478914040036}
Linking options:
https://www.mathnet.ru/eng/sjim842
https://www.mathnet.ru/eng/sjim/v17/i3/p13
This publication is cited in the following 23 articles:
Dmitry L. Tkachev, SEMA SIMAI Springer Series, 34, Hyperbolic Problems: Theory, Numerics, Applications. Volume I, 2024, 373
D. L. Tkachev, A. V. Yegitov, E. A. Biberdorf, “Linear instability of a resting state of the magnetohydrodynamic flows of polymeric fluid in a cylindrical channel (generalized Vinogradov–Pokrovski model)”, Physics of Fluids, 36:9 (2024)
D. L. Tkachev, “The spectrum and Lyapunov linear instability of the stationary state for polymer fluid flows: the Vinogradov–Pokrovskii model”, Siberian Math. J., 64:2 (2023), 407–423
D.L. Tkachev, “Spectrum and linear Lyapunov instability of a resting state for flows of an incompressible polymeric fluid”, Journal of Mathematical Analysis and Applications, 522:1 (2023), 126914
Blokhin A.M., Tkachev D.L., Yegitov A.V., “Lyapunov Instability of the Stationary Flows of a Polymeric Fluid in An Infinite Plane Channel With Constant Flow Rate”, J. Math. Anal. Appl., 506:1 (2022), 125541
Blokhin A.M., Tkachev D.L., “Mhd Model of Incompressible Polymeric Fluid. Linear Instability of the Resting State”, Complex Var. Elliptic Equ., 66:6-7, SI (2021), 929–944
Blokhin A.M., Tkachev D.L., “Lyapunov Instability of the Stationary Flows of Polymeric Fluid With Constant Flow Rate”, ZAMM-Z. Angew. Math. Mech., 101:12 (2021), e202000384
Alexander Blokhin, Dmitry Tkachev, INTERNATIONAL CONFERENCE ON THE METHODS OF AEROPHYSICAL RESEARCH (ICMAR 2020), 2351, INTERNATIONAL CONFERENCE ON THE METHODS OF AEROPHYSICAL RESEARCH (ICMAR 2020), 2021, 040057
A. M. Blokhin, A. S. Rudometova, D. L. Tkachev, “An MHD model of an incompressible polymeric fluid:
linear instability of a steady state”, J. Appl. Industr. Math., 14:3 (2020), 430–442
Blokhin A.M., Tkachev D.L., “Stability of the Poiseuille-Type Flow For a Mhd Model of An Incompressible Polymeric Fluid”, Eur. J. Mech. B-Fluids, 80 (2020), 112–121
A. M. Blokhin, D. L. Tkachev, Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy, 2020, 45
Alexander Blokhin, Dmitry Tkachev, “MHD model of an incompressible polymeric fluid. Linear instability of the resting state”, J. Phys.: Conf. Ser., 1666:1 (2020), 012007
V. V. Privalova, E. Yu. Prosviryakov, M. A. Simonov, “Nonlinear Gradient Flow of a Vertical Vortex Fluid in a Thin Layer”, Rus. J. Nonlin. Dyn., 15:3 (2019), 271–283
A. M. Blokhin, D. L. Tkachev, “Stability of Poiseuille-type flows for an MHD model of an incompressible polymeric fluid”, J. Hyberbolic Differ. Equ., 16:4 (2019), 793–817
A. M. Blokhin, D. L. Tkachev, “Stability of Poiseuille-type flows for an MHD model of an incompressible polymeric fluid”, Fluid Dyn., 54:8 (2019), 1051–1058
A. M. Blokhin, A. V. Yegitov, D. L. Tkachev, “Asymptotics of the spectrum of a linearized problem of the stability of a stationary flow of an incompressible polymer fluid with a space charge”, Comput. Math. Math. Phys., 58:1 (2018), 102–117
A. M. Blokhin, D. L. Tkachev, A. V. Yegitov, “Asymptotic formula for the spectrum of the linear problem describing periodic polymer flows in an infinite channel”, J. Appl. Mech. Tech. Phys., 59:6 (2018), 992–1003
A. Blokhin, D. Tkachev, A. Yegitov, “Spectral asymptotics of a linearized problem for an incompressible weakly conducting polymeric fluid”, ZAMM-Z. Angew. Math. Mech., 98:4 (2018), 589–601
Alexander Blokhin, Dmitry Tkachev, AIP Conference Proceedings, 2027, 2018, 030028