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On Solutions of the One-Dimensional Goldshtik Problem

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Abstract

A one-dimensional analog of the Goldshtik mathematical model for separated flows in an incompressible fluid is considered. The model is a boundary value problem for a second-order ordinary differential equation with discontinuous right-hand side. Some properties of the solutions of the problem, as well as the properties of the energy functional for different values of vorticity, are established. An approximate solution of the boundary value problem under study is found using the shooting method.

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Funding

This work was supported by the Russian Science Foundation under grant no. 23-21-00069, https://rscf.ru/en/project/23-21-00069/.

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Authors and Affiliations

  1. Saint Petersburg State University, Saint Petersburg, 199034, Russia

    O. V. Baskov & D. K. Potapov

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  1. O. V. Baskov
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  2. D. K. Potapov
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Correspondence to D. K. Potapov.

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The authors of this work declare that they have no conflicts of interest.

Additional information

Translated from Matematicheskie Zametki, 2024, Vol. 115, pp. 14–23 https://doi.org/10.4213/mzm13890.

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Baskov, O.V., Potapov, D.K. On Solutions of the One-Dimensional Goldshtik Problem. Math Notes 115, 12–20 (2024). https://doi.org/10.1134/S0001434624010024

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