Abstract
The problems of constructing exact solutions for the Navier–Stokes equations are related not only to the nonlinearity of the hydrodynamic equations, but also to their vector nature. In this paper, we propose a method for systematic constructing exact solutions to the linearized Navier–Stokes equations in the case of viscous flows by the eigenfunction expansion of Hermitian operators. As an example, the corresponding basis for the flow in the inner region of the circle is constructed. For clarity, expressions and graphs of current functions for individual modes are given. The obtained solutions can be used as test solutions for computer modeling of viscous fluid flows.
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Funding
This study was supported in part by the Russian Foundation for Basic Research and the Administration of the Udmurt Republic (project no. 18-42-180002).
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Translated by N. Wadhwa
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Vaskin, V.V., Lebedev, V.G., Ivanova, T.B. et al. Exact Solutions for Incompressible Viscous Fluid: Basis Expansion. Tech. Phys. 67, 618–623 (2022). https://doi.org/10.1134/S1063784222080102
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DOI: https://doi.org/10.1134/S1063784222080102