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Generalized sedeonic equations of hydrodynamics

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Abstract

We present a generalization of the equations of hydrodynamics based on the noncommutative algebra of space-time sedeons. It is shown that for vortex-less flow the system of Euler and continuity equations is represented as a single nonlinear sedeonic second-order wave equation for scalar and vector potentials, which is naturally generalized on viscous and vortex flows. As a result we obtained the closed system of four equations describing the diffusion damping of translational and vortex motions. The main peculiarities of the obtained equations are illustrated on the basis of the plane wave solutions describing the propagation of sound waves.

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Acknowledgements

We are very thankful to Galina Mironova for support and to reviewer for valuable and stimulating comments. Also we send our special thanks to EPJP editor Professor Tim Sluckin for suggestions and kind cooperation

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Authors and Affiliations

  1. Institute for Physics of Microstructures, Russian Academy of Sciences, GSP-105, Nizhny Novgorod, 603950, Russia

    V. L. Mironov & S. V. Mironov

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  1. V. L. Mironov
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  2. S. V. Mironov
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Correspondence to V. L. Mironov.

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Mironov, V.L., Mironov, S.V. Generalized sedeonic equations of hydrodynamics. Eur. Phys. J. Plus 135, 708 (2020). https://doi.org/10.1140/epjp/s13360-020-00700-5

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