Geodesic
Flows of a polymer fluid in domain with impermeable boundaries
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 10, pp. 1648-1655 
E. S. Baranovskii. Flows of a polymer fluid in domain with impermeable boundaries. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 10, pp. 1648-1655. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_10_a9/
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     title = {Flows of a polymer fluid in domain with impermeable boundaries},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Nonlinear boundary value problems modeling steady polymer flows in domains with impermeable solid walls are studied. The solvability of a nonhomogeneous boundary value problem for the equations governing a polymer flow in the case of an impermeable boundary is proved. The norms of solutions are estimated. The set of weak solutions is shown to be sequentially weakly closed. Additionally, explicit formulas are found for computing the solution of the boundary value problem describing the polymer flow induced by a stretching (shrinking) sheet.

[1] Pavlovskii V. A., “K voprosu o teoreticheskom opisanii slabykh vodnykh rastvorov polimerov”, Dokl. AN SSSR, 200:4 (1971), 809–812

[2] Oskolkov A. P., “O edinstvennosti i razreshimosti v tselom kraevykh zadach dlya uravnenii dvizheniya vodnykh rastvorov polimerov”, Kraevye zadachi matem. fiz. i smezhnye voprosy teorii funktsii. 7, Zap. nauchn. sem. LOMI, 38, 1973, 98–136

[3] Oskolkov A. P., “O nestatsionarnykh techeniyakh vyazko-uprugikh zhidkostei”, Kraevye zadachi matematicheskoi fiziki. 12, Tr. MIAN SSSR, 159, 1983, 103–131

[4] Sviridyuk G. A., Sukacheva T. G., “O razreshimosti nestatsionarnoi zadachi dinamiki neszhimaemoi vyazkouprugoi zhidkosti”, Matem. zametki, 63:3 (1998), 442–450 | DOI

[5] Korpusov M. O., Sveshnikov A. G., “O razrushenii resheniya sistemy uravnenii Oskolkova”, Matem. sb., 200:4 (2009), 83–108 | DOI

[6] Baranovskii E. S., “Issledovanie matematicheskikh modelei, opisyvayuschikh techeniya zhidkosti Foigta s lineinoi zavisimostyu komponent skorosti ot dvukh prostranstvennykh peremennykh”, Vestn. VGU. Seriya: Fizika. Matematika, 2011, no. 1, 77–93

[7] Ladyzhenskaya O. A., “O globalnoi odnoznachnoi razreshimosti dvumernykh zadach dlya vodnykh rastvorov polimerov”, Kraevye zadachi matem. fiz. i smezhnye voprosy teorii funktsii. 28, Zap. nauchn. sem. POMI, 243, 1997, 138–153

[8] Temam R., Uravneniya Nave–Stoksa. Teoriya i chislennyi analiz, Mir, M., 1981

[9] Lions Zh. L., Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972

[10] Galdi G. P., An introduction to the mathematical theory of the Navier–Stokes equations. Steady-state problems, Springer, New York, 2011

[11] Lions Zh. L., Madzhenes E., Neodnorodnye granichnye zadachi i ikh prilozheniya, Mir, M., 1971

[12] Gaevskii Kh., Greger K., Zakharias K., Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Mir, M., 1978

[13] Adams R. A., Fournier J. J. F., Sobolev spaces, 2nd ed., Elsevier, Amsterdam, 2003

[14] Sakiadis V. S., “Boundary-layer behavior on continuous solid surfaces. I: Boundary-layer equations for two-dimensional and axisymmetric flow”, AIChE J., 7 (1961), 26–28 | DOI

[15] Crane L. J., “Flow past a stretching plate”, Z. Angew Math. Phys., 21 (1970), 645–647 | DOI

[16] Sajid M., “Homotopy analysis of stretching flows with partial slip”, Int. J. of Nonlinear Sci., 8:3 (2009), 284–290

[17] Weidman P. D., Magyari E., “Generalized Crane flow induced by continuous surfaces stretching with arbitrary velocities”, Acta Mechanica, 209:3–4 (2010), 353–362 | DOI