Geodesic
On the Voitkunskii--Amfilokhiev--Pavlovskii model of motion of aqueous polymer solutions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems and methods in mechanics, Tome 300 (2018), pp. 176-189

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We study the mathematical properties of the model of motion of aqueous polymer solutions (Voitkunskii, Amfilokhiev, Pavlovskii, 1970) and its modifications in the limiting case of small relaxation times (Pavlovskii, 1971). In both cases, we examine plane unsteady laminar flows. In the first case, the properties of the flows are similar to those of the flow of an ordinary viscous fluid. In the second case, there may exist weak discontinuities that are preserved during the motion. We also address the steady flow problem for a dilute aqueous polymer solution moving in a cylindrical tube under a longitudinal pressure gradient. In this case, a flow with rectilinear trajectories (an analog of the classical Poiseuille flow) is possible. However, in contrast to the latter, the pressure in this flow depends on all three spatial variables. 
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     author = {V. V. Pukhnachev and O. A. Frolovskaya},
     title = {On the {Voitkunskii--Amfilokhiev--Pavlovskii} model of motion of aqueous polymer solutions},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {176--189},
     publisher = {mathdoc},
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     year = {2018},
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     url = {http://geodesic.mathdoc.fr/item/TM_2018_300_a13/}
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V. V. Pukhnachev; O. A. Frolovskaya. On the Voitkunskii--Amfilokhiev--Pavlovskii model of motion of aqueous polymer solutions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems and methods in mechanics, Tome 300 (2018), pp. 176-189. http://geodesic.mathdoc.fr/item/TM_2018_300_a13/