Applications of Group Analysis to the Three-Dimensional Equations of Fluids with Internal Inertia
Group classification of the three-dimensional equations describing flows of fluids with internal inertia, where the potential function W = W(ρ,ρ·), is presented. The given equations include such models as the non-linear one-velocity model of a bubbly fluid with incompressible liquid phase at small v...
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| Date: | 2008 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2008
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/149043 |
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| Cite this: | Applications of Group Analysis to the Three-Dimensional Equations of Fluids with Internal Inertia / P. Siriwat, S.V. Meleshko // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 22 назв. — англ. |
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irk-123456789-1490432019-02-20T01:28:37Z Applications of Group Analysis to the Three-Dimensional Equations of Fluids with Internal Inertia Siriwat, P. Meleshko, S.V. Group classification of the three-dimensional equations describing flows of fluids with internal inertia, where the potential function W = W(ρ,ρ·), is presented. The given equations include such models as the non-linear one-velocity model of a bubbly fluid with incompressible liquid phase at small volume concentration of gas bubbles, and the dispersive shallow water model. These models are obtained for special types of the function W(ρ,ρ·). Group classification separates out the function W(ρ,ρ·) at 15 different cases. Another part of the manuscript is devoted to one class of partially invariant solutions. This solution is constructed on the base of all rotations. In the gas dynamics such class of solutions is called the Ovsyannikov vortex. Group classification of the system of equations for invariant functions is obtained. Complete analysis of invariant solutions for the special type of a potential function is given. 2008 Article Applications of Group Analysis to the Three-Dimensional Equations of Fluids with Internal Inertia / P. Siriwat, S.V. Meleshko // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 22 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 76M60; 35Q35 http://dspace.nbuv.gov.ua/handle/123456789/149043 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Group classification of the three-dimensional equations describing flows of fluids with internal inertia, where the potential function W = W(ρ,ρ·), is presented. The given equations include such models as the non-linear one-velocity model of a bubbly fluid with incompressible liquid phase at small volume concentration of gas bubbles, and the dispersive shallow water model. These models are obtained for special types of the function W(ρ,ρ·). Group classification separates out the function W(ρ,ρ·) at 15 different cases. Another part of the manuscript is devoted to one class of partially invariant solutions. This solution is constructed on the base of all rotations. In the gas dynamics such class of solutions is called the Ovsyannikov vortex. Group classification of the system of equations for invariant functions is obtained. Complete analysis of invariant solutions for the special type of a potential function is given. |
| format |
Article |
| author |
Siriwat, P. Meleshko, S.V. |
| spellingShingle |
Siriwat, P. Meleshko, S.V. Applications of Group Analysis to the Three-Dimensional Equations of Fluids with Internal Inertia Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Siriwat, P. Meleshko, S.V. |
| author_sort |
Siriwat, P. |
| title |
Applications of Group Analysis to the Three-Dimensional Equations of Fluids with Internal Inertia |
| title_short |
Applications of Group Analysis to the Three-Dimensional Equations of Fluids with Internal Inertia |
| title_full |
Applications of Group Analysis to the Three-Dimensional Equations of Fluids with Internal Inertia |
| title_fullStr |
Applications of Group Analysis to the Three-Dimensional Equations of Fluids with Internal Inertia |
| title_full_unstemmed |
Applications of Group Analysis to the Three-Dimensional Equations of Fluids with Internal Inertia |
| title_sort |
applications of group analysis to the three-dimensional equations of fluids with internal inertia |
| publisher |
Інститут математики НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149043 |
| citation_txt |
Applications of Group Analysis to the Three-Dimensional Equations of Fluids with Internal Inertia / P. Siriwat, S.V. Meleshko // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 22 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT siriwatp applicationsofgroupanalysistothethreedimensionalequationsoffluidswithinternalinertia AT meleshkosv applicationsofgroupanalysistothethreedimensionalequationsoffluidswithinternalinertia |
| first_indexed |
2025-07-12T20:58:49Z |
| last_indexed |
2025-07-12T20:58:49Z |
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