Geodesic
Spectrum of a problem about the flow of a polymeric viscoelastic fluid in a cylindrical channel (Vinogradov-Pokrovski model)
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 1269-1289

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We study the linear stability of a resting state for flows of incompressible viscoelastic polymeric fluid in an infinite cylindrical channel in axisymmetric perturbation class. We use structurally-phenomenological Vinogradov-Pokrovski model as our mathematical model. We formulate two equations that define the spectrum of the problem. Our numerical experiments show that with the growth of perturbations frequency along the channel axis there appear eigenvalues with positive real part for the radial velocity component of the first spectral equation. That guarantees linear Lyapunov instability of the resting state.
Keywords: incompressible viscoelastic polymeric medium, rheological correlation, resting state, linearized mixed problem, Lyapunov stability. 
@article{SEMR_2023_20_2_a48,
     author = {D. L. Tkachev and E. A. Biberdorf},
     title = {Spectrum of a problem about the flow of a polymeric viscoelastic fluid in a cylindrical channel {(Vinogradov-Pokrovski} model)},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1269--1289},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2023},
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     url = {http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a48/}
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D. L. Tkachev; E. A. Biberdorf. Spectrum of a problem about the flow of a polymeric viscoelastic fluid in a cylindrical channel (Vinogradov-Pokrovski model). Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 1269-1289. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a48/