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Abstract <p> The time evolution of a system of small perturbations imposed on a triaxial homogeneousspreading–drain in an infinite three-dimensional space of a Newtonian incompressible fluid isinvestigated. In the first part of the paper, it is assumed that the main motion is stationary andthe velocity field is defined by only two constants. In this case, the linearized problem for thevelocity and pressure perturbations is reduced to a spectral problem in which the real part of thespectral parameter is related to the nature of the exponential decay or growth of the initialperturbations. Based on the method of integral relations for quadratic functionals, an upperbound for this parameter is obtained. In the second part of the paper, a more general case ofunsteady triaxial spreading–drain is considered. For the perturbation growth, we derive an upperintegral bound that includes a time function completely determined by the velocity field of themain fluid flow.</p>

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Upper Estimates of the Perturbation Growth under Triaxial Spreading–Drain in Infinite Viscous Space

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • D. V. Georgievskii

摘要

Abstract

The time evolution of a system of small perturbations imposed on a triaxial homogeneousspreading–drain in an infinite three-dimensional space of a Newtonian incompressible fluid isinvestigated. In the first part of the paper, it is assumed that the main motion is stationary andthe velocity field is defined by only two constants. In this case, the linearized problem for thevelocity and pressure perturbations is reduced to a spectral problem in which the real part of thespectral parameter is related to the nature of the exponential decay or growth of the initialperturbations. Based on the method of integral relations for quadratic functionals, an upperbound for this parameter is obtained. In the second part of the paper, a more general case ofunsteady triaxial spreading–drain is considered. For the perturbation growth, we derive an upperintegral bound that includes a time function completely determined by the velocity field of themain fluid flow.