Research output: Contribution to journal › Article › peer-review
Exact Solutions of Second-Grade Fluid Equations. / Petrova, A. G.; Pukhnachev, V. V.; Frolovskaya, O. A.
In: Proceedings of the Steklov Institute of Mathematics, Vol. 322, No. 1, 09.2023, p. 173-187.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Exact Solutions of Second-Grade Fluid Equations
AU - Petrova, A. G.
AU - Pukhnachev, V. V.
AU - Frolovskaya, O. A.
N1 - Публикация для корректировки.
PY - 2023/9
Y1 - 2023/9
N2 - The second-grade fluid equations describe the motion of relaxing fluids such as aqueous solutions of polymers. The existence and uniqueness of solutions to the initial–boundary value problems for these equations were studied by D. Cioranescu, V. Girault, C. Le Roux, A. Tani, G. P. Galdi, and others. However, their studies do not contain information about the qualitative properties of solutions of these equations. Such information can be obtained by analyzing their exact solutions, which is the main goal of this work. We study layered flows and a model problem with a free boundary, construct an analog of T. Kármán’s solution, which describes the stationary motion of a second-grade fluid in a half-space induced by the rotation of the plane bounding it, and propose a generalization of V. A. Steklov’s solution of the problem on unsteady helical flows of a Newtonian fluid to the case of a second-grade fluid.
AB - The second-grade fluid equations describe the motion of relaxing fluids such as aqueous solutions of polymers. The existence and uniqueness of solutions to the initial–boundary value problems for these equations were studied by D. Cioranescu, V. Girault, C. Le Roux, A. Tani, G. P. Galdi, and others. However, their studies do not contain information about the qualitative properties of solutions of these equations. Such information can be obtained by analyzing their exact solutions, which is the main goal of this work. We study layered flows and a model problem with a free boundary, construct an analog of T. Kármán’s solution, which describes the stationary motion of a second-grade fluid in a half-space induced by the rotation of the plane bounding it, and propose a generalization of V. A. Steklov’s solution of the problem on unsteady helical flows of a Newtonian fluid to the case of a second-grade fluid.
KW - boundary layer
KW - free boundary problems
KW - helical motions
KW - layered flows
KW - second-grade fluid
UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85180234830&origin=inward&txGid=f2262cdc4bf134bd7f41c9c391f9efe3
UR - https://www.mendeley.com/catalogue/165e22c3-75f3-3941-9cdb-a293320adb92/
U2 - 10.1134/S0081543823040156
DO - 10.1134/S0081543823040156
M3 - Article
VL - 322
SP - 173
EP - 187
JO - Proceedings of the Steklov Institute of Mathematics
JF - Proceedings of the Steklov Institute of Mathematics
SN - 0081-5438
IS - 1
ER -
ID: 59549216