Abstract

This paper is devoted to small motions problem of composite hydrodynamic systems containing a viscoelastic fluid. Hydrodynamic systems of two or more viscoelastic fluids are considered, as well as partially dissipative systems containing ideal fluids or a barotropic gas (in addition to a viscoelastic fluid). The listed initial-boundary-value problems are investigated using the operator approach developed by N. D. Kopachevsky. This approach makes it possible to pass from the initial-boundary-value problem to the Cauchy problem for an operator-differential equation in the sum of Hilbert spaces and to prove the correct solvability theorem.

中文翻译：

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含有粘弹性流体的流体动力系统的小运动

摘要

本文致力于研究包含粘弹性流体的复合流体动力系统的小运动问题。考虑了两种或多种粘弹性流体的流体动力系统，以及包含理想流体或正压气体（除了粘弹性流体）的部分耗散系统。使用 ND Kopachevsky 开发的算子方法研究列出的初始边界值问题。这种方法可以将 Hilbert 空间和中的算子微分方程从初始边界值问题传递到柯西问题，并证明正确的可解性定理。