Abstract

This review paper is devoted to the description of the results of N.D. Kopachevsky and S. Krein (form 1964 till nowadays) related to spectral properties of strong dissipative hydrodynamical systems and corresponding operator-differential equations. Such spectral problems usually lead to eigenvalue problem for the so-called operator pencil of S. Krein with some possible modifications. We provide some abstract results for differential equations in Hilbert space, consider a number of problems on normal motions of a heavy viscous liquid under the different additional physical conditions, enumerate properties of the classical pencil of S. Krein and its modifications.

中文翻译：

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强耗散流体动力系统和 S. Kerin 的操作员铅笔

摘要

这篇综述论文致力于描述 ND Kopachevsky 和 ​​S. Kerin（1964 年至今）与强耗散流体动力学系统的光谱特性和相应的算子微分方程相关的结果。对于 S. Kerin 所谓的算子铅笔，这种谱问题通常会导致特征值问题，并进行一些可能的修改。我们为希尔伯特空间中的微分方程提供了一些抽象结果，考虑了在不同附加物理条件下重粘性液体的法向运动的一些问题，列举了 S. Kerin 经典铅笔的性质及其修改。