A. G. Petrova, V. V. Pukhnachev, O. A. Frolovskaya
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引用次数: 0
Abstract
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.
摘要 二级流体方程描述了聚合物水溶液等松弛流体的运动。D. Cioranescu、V. Girault、C. Le Roux、A. Tani、G. P. Galdi 等人研究了这些方程初界值问题解的存在性和唯一性。然而，他们的研究并不包含有关这些方程的解的定性属性的信息。这些信息可以通过分析其精确解来获得，而这正是本研究的主要目标。我们研究了层流和自由边界的模型问题，构建了 T. Kármán 的类似解，该解描述了第二级流体在其边界平面旋转引起的半空间中的静止运动，并提出了将 V. A. Steklov 的牛顿流体非稳态螺旋流动问题解推广到第二级流体的情况。
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