Geodesic
Couette Problem for Kelvin–Voigt Medium
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 3, pp. 94-109 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The analogue of classical Couette problem for incompressible viscoelastic Kelvin–Voigt medium motion in the gap between two coaxial cylinders is investigated. External cylinder is fixed, while the internal one is either rotating forcedly with a constant velocity or rotating inertially. Unique solvability is proved for both problems. The analogy between propagation of acoustic cylindrical waves in viscous gas and transversal waves in Kelvin–Voigt medium which appear during its motion along circular trajectories is found. The asymptotic behavior of solution stabilization to Couette motion in the first problem and inertial cylinder motion approaching to equilibrium state were studied. Both monotonous and oscillatory regimes of quiescent state approaching are possible subject to problem parameters.
Keywords: viscoelasticity, incompressibility, Cjuette problem, acoustic analogy, sptectral problem, asymptotics at large time.
Mots-clés : Kelvin–Foigt medium 
@article{VNGU_2010_10_3_a6,
     author = {V. V. Pukhnachev and T. P. Pukhnacheva},
     title = {Couette {Problem} for {Kelvin{\textendash}Voigt} {Medium}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {94--109},
     year = {2010},
     volume = {10},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2010_10_3_a6/}
}
TY  - JOUR
AU  - V. V. Pukhnachev
AU  - T. P. Pukhnacheva
TI  - Couette Problem for Kelvin–Voigt Medium
JO  - Sibirskij žurnal čistoj i prikladnoj matematiki
PY  - 2010
SP  - 94
EP  - 109
VL  - 10
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VNGU_2010_10_3_a6/
LA  - ru
ID  - VNGU_2010_10_3_a6
ER  - 
%0 Journal Article
%A V. V. Pukhnachev
%A T. P. Pukhnacheva
%T Couette Problem for Kelvin–Voigt Medium
%J Sibirskij žurnal čistoj i prikladnoj matematiki
%D 2010
%P 94-109
%V 10
%N 3
%U http://geodesic.mathdoc.fr/item/VNGU_2010_10_3_a6/
%G ru
%F VNGU_2010_10_3_a6
V. V. Pukhnachev; T. P. Pukhnacheva. Couette Problem for Kelvin–Voigt Medium. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 3, pp. 94-109. http://geodesic.mathdoc.fr/item/VNGU_2010_10_3_a6/

[1] Reiner M., Reologiya, Nauka, M., 1965

[2] Rabotnov Yu. N., Elementy nasledstvennoi mekhaniki tverdykh tel, Nauka, M., 1977 | MR

[3] Joseph D. D., Fluid Dynamics of Viscoelastic Liquids, Springer-Verlag, 1990 | MR

[4] Zhermen P., Kurs mekhaniki sploshnykh sred, Vysshaya shkola, M., 1963

[5] Gorodtsov V. A., Leonov A. I., “O kinematike, neravnovesnoi termodinamike i reologicheskikh sootnosheniyakh v nelineinoi teorii vyazko-uprugosti”, PMM, 32:1 (1968), 70–94 | Zbl

[6] Kluitenberg J. A., “A Unified Thermodinamic Theory for Large Deformations in Elastic Media and in Kelvin(Voight) Media and for Viscous Fluid Flow”, Physica, 30:10a (1964) | DOI | MR | Zbl

[7] Osipov S. V., “Zadacha o zapolnenii sfericheskoi polosti v srede Kelvina–Foigta”, PMTF, 49:5 (2008), 93–101 | MR

[8] Kochin N. E., Kibel I. A., Roze N. V., Teoreticheskaya gidromekhanika, v. 2, GIFML, M., 1963

[9] Landau L. D., Lifshits E. M., Teoreticheskaya fizika, v. 6, Gidrodinamika, Nauka, M., 1986 | MR

[10] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967 | MR

[11] Yanke E., Emde F., Tablitsy funktsii s formulami i krivymi, GIFML, M., 1959