Complete integrability of a hydrodynamic Navier-Stokes model of the flow in a two-dimensional incompressible ideal liquid with a free surface
We establish the complete integrability of a nonlinear dynamical system associated with the hydrodynamic Navier-Stokes equations for the flow of an ideal two-dimensional liquid with a free surface over the horizontal bottom. We show that this dynamical system is naturally connected with the nonlinea...
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| Datum: | 1993 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1993
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5786 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512011481251840 |
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| author | Samoilenko, V. G. Suyarov, U. S. Самойленко, В. Г. Суяров, У. С. Самойленко, В. Г. Суяров, У. С. |
| author_facet | Samoilenko, V. G. Suyarov, U. S. Самойленко, В. Г. Суяров, У. С. Самойленко, В. Г. Суяров, У. С. |
| author_sort | Samoilenko, V. G. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:17:59Z |
| description | We establish the complete integrability of a nonlinear dynamical system associated with the hydrodynamic Navier-Stokes equations for the flow of an ideal two-dimensional liquid with a free surface over the horizontal bottom. We show that this dynamical system is naturally connected with the nonlinear kinetic Boltzmann-Vlasov equation for a one-dimensional flow of particles with a point potential of interaction between particles. |
| first_indexed | 2026-03-24T03:22:00Z |
| format | Article |
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| id | umjimathkievua-article-5786 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:22:00Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/23/be0c0ec23ccbe71d219478d20656cc23.pdf |
| spelling | umjimathkievua-article-57862020-03-19T09:17:59Z Complete integrability of a hydrodynamic Navier-Stokes model of the flow in a two-dimensional incompressible ideal liquid with a free surface Полная интегрируемость одной гидродинамической модели Навье - Стокса течения двухмерной несжимаемой идеальной жидкости со свободной поверхностью Samoilenko, V. G. Suyarov, U. S. Самойленко, В. Г. Суяров, У. С. Самойленко, В. Г. Суяров, У. С. We establish the complete integrability of a nonlinear dynamical system associated with the hydrodynamic Navier-Stokes equations for the flow of an ideal two-dimensional liquid with a free surface over the horizontal bottom. We show that this dynamical system is naturally connected with the nonlinear kinetic Boltzmann-Vlasov equation for a one-dimensional flow of particles with a point potential of interaction between particles. Встановлена повна інтегровність однієї нелінійної динамічної системи, асоційованої з гідродинамічними рівняннями Нав’є - Стокса течії ідеальної двовимірної рідини з вільною поверхнею над горизонтальним дном. Показано, що з даною динамічною системою природним чином пов’язане нелінійне кінетичне рівняння Больцмана - Власова для одновимірної течії частинок з точковим потенціалом взаємодії між частинками. Institute of Mathematics, NAS of Ukraine 1993-01-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5786 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 1 (1993); 86–90 Український математичний журнал; Том 45 № 1 (1993); 86–90 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5786/8256 https://umj.imath.kiev.ua/index.php/umj/article/view/5786/8257 Copyright (c) 1993 Samoilenko V. G.; Suyarov U. S. |
| spellingShingle | Samoilenko, V. G. Suyarov, U. S. Самойленко, В. Г. Суяров, У. С. Самойленко, В. Г. Суяров, У. С. Complete integrability of a hydrodynamic Navier-Stokes model of the flow in a two-dimensional incompressible ideal liquid with a free surface |
| title | Complete integrability of a hydrodynamic Navier-Stokes model of the flow in a two-dimensional incompressible ideal liquid with a free surface |
| title_alt | Полная интегрируемость одной гидродинамической модели Навье - Стокса течения двухмерной несжимаемой идеальной жидкости со свободной поверхностью |
| title_full | Complete integrability of a hydrodynamic Navier-Stokes model of the flow in a two-dimensional incompressible ideal liquid with a free surface |
| title_fullStr | Complete integrability of a hydrodynamic Navier-Stokes model of the flow in a two-dimensional incompressible ideal liquid with a free surface |
| title_full_unstemmed | Complete integrability of a hydrodynamic Navier-Stokes model of the flow in a two-dimensional incompressible ideal liquid with a free surface |
| title_short | Complete integrability of a hydrodynamic Navier-Stokes model of the flow in a two-dimensional incompressible ideal liquid with a free surface |
| title_sort | complete integrability of a hydrodynamic navier-stokes model of the flow in a two-dimensional incompressible ideal liquid with a free surface |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5786 |
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