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Orthogonality Relations for a Stationary Flow of an Ideal Fluid

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Abstract

For a real solution (u, p) to the Euler stationary equations for an ideal fluid, we derive an infinite series of the orthogonality relations that equate some linear combinations of mth degree integral momenta of the functions uiuj and p to zero (m = 0, 1,... ). In particular, the zeroth degree orthogonality relations state that the components ui of the velocity field are L2-orthogonal to each other and have coincident L2-norms. Orthogonality relations of degree m are valid for a solution belonging to a weighted Sobolev space with the weight depending on m.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, Russia

    V. A. Sharafutdinov

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  1. V. A. Sharafutdinov
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Correspondence to V. A. Sharafutdinov.

Additional information

Original Russian Text © 2018 Sharafutdinov V.A.

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, vol. 59, no. 4, pp. 927–952, July–August, 2018; DOI: 10.17377/smzh.2018.59.415.

The author was supported by the Russian Foundation for Basic Research (Grant 17–51–150001).

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Sharafutdinov, V.A. Orthogonality Relations for a Stationary Flow of an Ideal Fluid. Sib Math J 59, 731–752 (2018). https://doi.org/10.1134/S0037446618040158

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  • DOI: https://doi.org/10.1134/S0037446618040158

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