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Steady-State Flows of Ideal Incompressible Fluid with Velocity Pointwise Orthogonal to the Pressure Gradient Научная публикация

Журнал Arnold Mathematical Journal
ISSN: 2199-6792 , E-ISSN: 2199-6806
Вых. Данные Год: 2024, Том: 10, Номер: 2, Страницы: 223–256 Страниц : 34 DOI: 10.1007/s40598-023-00234-5
Ключевые слова Euler equations · Ideal fluid · Gavrilov flow · Geodesic vector field
Авторы Rovenski Vladimir 1,2 , Sharafutdinov V.A. 1,2
Организации
1 Sobolev Institute of Mathematics, 4 Koptyug Avenue, Novosibirsk, Russia
2 Department of Mathematics, University of Haifa, Haifa, Israel

Информация о финансировании (1)

1 Институт математики им. С.Л. Соболева СО РАН FWNF-2022-0006

Реферат: A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the velocity vector is orthogonal to the gradient of the pressure at any point. Such solutions are called Gavrilov flows. We describe the local structure of Gavrilov flows in terms of the geometry of isobaric hypersurfaces. In the 3D case, we obtain a system of PDEs for axisymmetric Gavrilov flows and find consistency conditions for the system. Two numerical examples of axisymmetric Gavrilov flows are presented: with pressure function periodic in the axial direction, and with isobaric surfaces diffeomorphic to the torus.
Библиографическая ссылка: Rovenski V. , Sharafutdinov V.A.
Steady-State Flows of Ideal Incompressible Fluid with Velocity Pointwise Orthogonal to the Pressure Gradient
Arnold Mathematical Journal. 2024. V.10. N2. P.223–256. DOI: 10.1007/s40598-023-00234-5 Scopus РИНЦ OpenAlex
Даты:
Поступила в редакцию: 16 февр. 2023 г.
Принята к публикации: 14 июл. 2023 г.
Опубликована online: 1 авг. 2023 г.
Опубликована в печати: 7 мар. 2024 г.
Идентификаторы БД:
Scopus: 2-s2.0-85166282951
РИНЦ: 63421548
OpenAlex: W4385462764
Цитирование в БД: Пока нет цитирований
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