Geodesic
Couette flow of a~viscoelastic Maxwell-type medium with two relaxation times
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems and methods in mechanics, Tome 300 (2018), pp. 146-157

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A Couette flow of a viscoelastic medium is considered that is described by the Johnson–Segalman–Oldroyd model with two relaxation times. The development of singularities related to the appearance of internal discontinuities is studied both analytically and numerically within one-dimensional nonstationary hyperbolic models of viscoelastic Maxwell-type media. A numerical model for calculating nonstationary one-dimensional discontinuous solutions is constructed, discontinuous solutions are studied, and the hysteresis phenomenon, i.e., the dependence of the structure of a steady Couette flow on the prehistory of its formation, is analyzed. 
@article{TM_2018_300_a10,
     author = {V. Yu. Liapidevskii},
     title = {Couette flow of a~viscoelastic {Maxwell-type} medium with two relaxation times},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {146--157},
     publisher = {mathdoc},
     volume = {300},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2018_300_a10/}
}
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V. Yu. Liapidevskii. Couette flow of a~viscoelastic Maxwell-type medium with two relaxation times. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems and methods in mechanics, Tome 300 (2018), pp. 146-157. http://geodesic.mathdoc.fr/item/TM_2018_300_a10/