Keywords: problem with a free boundary, solution breakdown.
@article{TMF_2022_211_2_a9,
author = {V. V. Pukhnachov},
title = {Strip deformation problem in three models of hydrodynamics},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {306--318},
year = {2022},
volume = {211},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2022_211_2_a9/}
}
V. V. Pukhnachov. Strip deformation problem in three models of hydrodynamics. Teoretičeskaâ i matematičeskaâ fizika, Tome 211 (2022) no. 2, pp. 306-318. http://geodesic.mathdoc.fr/item/TMF_2022_211_2_a9/
[1] L. V. Ovsyannikov, “Obschie uravneniya i primery”, Zadacha o neustanovivshemsya dvizhenii zhidkosti so svobodnoi granitsei, Nauka. Sib. otd., Novosibirsk, 1967, 5–75
[2] M. S. Longuet-Higgins, “A class of exact, time-dependent, free-surface flows”, J. Fluid Mech., 55:3 (1972), 529–543 | DOI | MR
[3] V. I. Nalimov, V. V. Pukhnachev, Neustanovivshiesya dvizheniya idealnoi zhidkosti so svobodnoi granitsei, Izd-vo Novosib. gos. un-ta, Novosibirsk, 1975
[4] S. Chandrasekkhar, Ellipsoidalnye figury ravnovesiya, Mir, M., 1973 | Zbl
[5] L. V. Ovsyannikov, “Ob odnom sluchae neustanovivshegosya dvizheniya so svobodnoi granitsei”, Dinamika sploshnoi sredy, Sb. nauchn. tr. Vyp. 12, Institut gidrodinamiki SO RAN, Novosibirsk, 1972, 124–130
[6] O. M. Lavrenteva, “O dvizhenii zhidkogo ellipsoida”, Dokl. AN SSSR, 253:4 (1980), 828–831 | MR | Zbl
[7] L. V. Ovsyannikov, “Ob odnom klasse neustanovivshikhsya dvizhenii neszhimaemoi zhidkosti”, Trudy V Sessii Uchenogo soveta po narodnokhozyaistvennomu ispolzovaniyu vzryva, Ilim, Frunze, 1965, 34–42
[8] O. M. Lavrenteva, “Ob odnom klasse dvizhenii zhidkogo ellipsoida”, PMTF, 25:4 (1984), 148–153 | DOI | MR
[9] V. V. Pukhnachev, “O dvizhenii zhidkogo ellipsa”, Dinamika sploshnoi sredy, Sb. nauchn. tr. Vyp. 33, Institut gidrodinamiki SO RAN, Novosibirsk, 1978, 68–75
[10] L. V. Ovsyannikov, Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978 | MR
[11] E. N. Zhuravleva, “Chislennoe issledovanie tochnogo resheniya uravnenii Nave–Stoksa, opisyvayuschego dvizhenie so svobodnoi granitsei”, PMTF, 57:3 (2016), 9–15 | DOI | MR
[12] V. V. Pukhnachev, E. N. Zhuravleva, “Viscous flows with flat free boundaries”, Eur. Phys. J. Plus, 135:7 (2020), 554, 12 pp. | DOI
[13] V. V. Pukhnachev, “On a problem of viscous strip deformation with a free boundary”, C. R. Acad. Sci. Paris. Sér. I Math., 328:4 (1999), 357–362 | DOI | MR
[14] V. A. Pavlovskii, “K voprosu o teoreticheskom opisanii slabykh vodnykh rastvorov polimerov”, Dokl. AN SSSR, 200:4 (1971), 809–812
[15] O. A. Frolovskaya, “Dvizhenie vodnogo rastvora polimera so svobodnoi granitsei”, PMTF, 63:1 (2022), 40–49
[16] A. G. Petrova, V. V. Pukhnachev, “Free boundary problem in a polymer solution model”, Russian J. Math. Phys., 28:1 (2021), 96–103 | DOI | MR