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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2008 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2008
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149043 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-149043 |
|---|---|
| record_format |
dspace |
| spelling |
Siriwat, P. Meleshko, S.V. 2019-02-19T13:14:28Z 2019-02-19T13:14:28Z 2008 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 https://nasplib.isofts.kiev.ua/handle/123456789/149043 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. This paper is a contribution to the Proceedings of the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” (June 24–30, 2007, Kyiv, Ukraine). The work of P.S. has been supported by scholarship of the Ministry of University Af fairs of Thailand. The authors also thank S.L. Gavrilyuk for fruitful discussions, and E. Schulz for his kind help. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Applications of Group Analysis to the Three-Dimensional Equations of Fluids with Internal Inertia Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Applications of Group Analysis to the Three-Dimensional Equations of Fluids with Internal Inertia |
| spellingShingle |
Applications of Group Analysis to the Three-Dimensional Equations of Fluids with Internal Inertia Siriwat, P. Meleshko, S.V. |
| 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 |
| author |
Siriwat, P. Meleshko, S.V. |
| author_facet |
Siriwat, P. Meleshko, S.V. |
| publishDate |
2008 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.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. |
| work_keys_str_mv |
AT siriwatp applicationsofgroupanalysistothethreedimensionalequationsoffluidswithinternalinertia AT meleshkosv applicationsofgroupanalysistothethreedimensionalequationsoffluidswithinternalinertia |
| first_indexed |
2025-12-01T11:30:57Z |
| last_indexed |
2025-12-01T11:30:57Z |
| _version_ |
1850860141559152640 |