Kahler Geometry and Burgers' Vortices
We study the Navier-Stokes and Euler equations of incompressible hydrodynamics. Taking the divergence of the momentum equation leads, as usual, to a Poisson equation for the pressure: in this paper we study this equation in two spatial dimensions using Monge-Ampere structures. In two dimensional flo...
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| Дата: | 2009 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
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Інститут математики НАН України
2009
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/6310 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Kahler Geometry and Burgers' Vortices / I. Roulstone, B. Banos, J.D. Gibbon, V.N. Roubtsov // Збірник праць Інституту математики НАН України. — 2009. — Т. 6, № 2. — С. 303-321. — Бібліогр.: 30 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862730097761452032 |
|---|---|
| author | Roulstone, I. Banos, B. Gibbon, J.D. Roubtsov, V.N. |
| author_facet | Roulstone, I. Banos, B. Gibbon, J.D. Roubtsov, V.N. |
| citation_txt | Kahler Geometry and Burgers' Vortices / I. Roulstone, B. Banos, J.D. Gibbon, V.N. Roubtsov // Збірник праць Інституту математики НАН України. — 2009. — Т. 6, № 2. — С. 303-321. — Бібліогр.: 30 назв. — англ. |
| collection | DSpace DC |
| description | We study the Navier-Stokes and Euler equations of incompressible hydrodynamics. Taking the divergence of the momentum equation leads, as usual, to a Poisson equation for the pressure: in this paper we study this equation in two spatial dimensions using Monge-Ampere structures. In two dimensional flows where the Laplacian of the pressure is positive, a Kahler geometry is described on the phase space of the fluid; in regions where the Laplacian of the pressure is negative, a product structure is described. These structures can be related to the ellipticity and hyperbolicity (respectively) of a Monge-Ampere equation. We then show how this structure can be extended to a class of canonical vortex structures in three dimensions.
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| first_indexed | 2025-12-07T19:17:59Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-6310 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-2910 |
| language | English |
| last_indexed | 2025-12-07T19:17:59Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Roulstone, I. Banos, B. Gibbon, J.D. Roubtsov, V.N. 2010-02-23T14:32:25Z 2010-02-23T14:32:25Z 2009 Kahler Geometry and Burgers' Vortices / I. Roulstone, B. Banos, J.D. Gibbon, V.N. Roubtsov // Збірник праць Інституту математики НАН України. — 2009. — Т. 6, № 2. — С. 303-321. — Бібліогр.: 30 назв. — англ. 1815-2910 https://nasplib.isofts.kiev.ua/handle/123456789/6310 We study the Navier-Stokes and Euler equations of incompressible hydrodynamics. Taking the divergence of the momentum equation leads, as usual, to a Poisson equation for the pressure: in this paper we study this equation in two spatial dimensions using Monge-Ampere structures. In two dimensional flows where the Laplacian of the pressure is positive, a Kahler geometry is described on the phase space of the fluid; in regions where the Laplacian of the pressure is negative, a product structure is described. These structures can be related to the ellipticity and hyperbolicity (respectively) of a Monge-Ampere equation. We then show how this structure can be extended to a class of canonical vortex structures in three dimensions. en Інститут математики НАН України Геометрія, топологія та їх застосування Праці міжнародної конференції "Геометрія в Одесі - 2008" Kahler Geometry and Burgers' Vortices Article published earlier |
| spellingShingle | Kahler Geometry and Burgers' Vortices Roulstone, I. Banos, B. Gibbon, J.D. Roubtsov, V.N. Геометрія, топологія та їх застосування Праці міжнародної конференції "Геометрія в Одесі - 2008" |
| title | Kahler Geometry and Burgers' Vortices |
| title_full | Kahler Geometry and Burgers' Vortices |
| title_fullStr | Kahler Geometry and Burgers' Vortices |
| title_full_unstemmed | Kahler Geometry and Burgers' Vortices |
| title_short | Kahler Geometry and Burgers' Vortices |
| title_sort | kahler geometry and burgers' vortices |
| topic | Геометрія, топологія та їх застосування Праці міжнародної конференції "Геометрія в Одесі - 2008" |
| topic_facet | Геометрія, топологія та їх застосування Праці міжнародної конференції "Геометрія в Одесі - 2008" |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/6310 |
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