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 -