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Euler Continuity Equation with High-Order Terms in Time

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Abstract

In this paper, we examine the appearance of high-order terms in the continuity equation for an incompressible fluid obtained by L. Euler in 1752 from the linear Cauchy–Helmholtz equations. Solution of the inhomogeneous wave equation allows one calculate or estimate the intensity of vibrations and self-oscillations, which are sometimes considered spontaneous.

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Authors and Affiliations

  1. Moscow State Academy of Water Transport, Moscow, Russia

    V. M. Ovsyannikov

  2. Noyabrsk Institute of Oil and Gas — Branch of Tyumen Industrial University, Noyabrsk, Russia

    V. M. Ovsyannikov

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  1. V. M. Ovsyannikov
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Correspondence to V. M. Ovsyannikov.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 182, Proceedings of the International Conference “Classical and Modern Geometry” Dedicated to the 100th Anniversary of Professor V. T. Bazylev. Moscow, April 22-25, 2019. Part 4, 2020.

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Ovsyannikov, V.M. Euler Continuity Equation with High-Order Terms in Time. J Math Sci 277, 798–803 (2023). https://doi.org/10.1007/s10958-023-06888-y

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  • DOI: https://doi.org/10.1007/s10958-023-06888-y

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