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Applications of Group Analysis to the Three-Dimensional Equations of Fluids with Internal Inertia
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2008, том 4
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Applications of Group Analysis to the Three-Dimensional Equations of Fluids with Internal Inertia
Інший ID:
2000 Mathematics Subject Classification: 76M60; 35Q35
Посилання:
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.
Підтримка:
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.
Дата:
2008
Переглядів:
506
Завантажень:
249
Анотація:
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.
