Research output: Contribution to journal › Article › peer-review
Special vortex in relativistic hydrodynamics. / Chupakhin, A. P.; Yanchenko, A. A.
In: Journal of Physics: Conference Series, Vol. 894, No. 1, 012114, 22.10.2017.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Special vortex in relativistic hydrodynamics
AU - Chupakhin, A. P.
AU - Yanchenko, A. A.
PY - 2017/10/22
Y1 - 2017/10/22
N2 - An exact solution of the Euler equations governing the flow of a compressible fluid in relativistic hydrodynamics is found and studied. It is a relativistic analogue of the Ovsyannikov vortex (special vortex) investigated earlier for classical gas dynamics. Solutions are partially invariant of Defect 1 and Rank 2 with respect to the rotation group. A theorem on the representation of the factor-system in the form of a union of a non-invariant subsystem for the function determining the deviation of the velocity vector from the meridian, and invariant subsystem for determination of thermodynamic parameters, the Lorentz factor and the radial velocity component is proved. Compatibility conditions for the overdetermined non-invariant subsystem are obtained. A stationary solution of this type is studied in detail. It is proved that its invariant subsystem reduces to an implicit differential equation. For this equation, the manifold of branching of solutions is investigated, and a set of singular points is found.
AB - An exact solution of the Euler equations governing the flow of a compressible fluid in relativistic hydrodynamics is found and studied. It is a relativistic analogue of the Ovsyannikov vortex (special vortex) investigated earlier for classical gas dynamics. Solutions are partially invariant of Defect 1 and Rank 2 with respect to the rotation group. A theorem on the representation of the factor-system in the form of a union of a non-invariant subsystem for the function determining the deviation of the velocity vector from the meridian, and invariant subsystem for determination of thermodynamic parameters, the Lorentz factor and the radial velocity component is proved. Compatibility conditions for the overdetermined non-invariant subsystem are obtained. A stationary solution of this type is studied in detail. It is proved that its invariant subsystem reduces to an implicit differential equation. For this equation, the manifold of branching of solutions is investigated, and a set of singular points is found.
UR - http://www.scopus.com/inward/record.url?scp=85033238431&partnerID=8YFLogxK
U2 - 10.1088/1742-6596/894/1/012114
DO - 10.1088/1742-6596/894/1/012114
M3 - Article
AN - SCOPUS:85033238431
VL - 894
JO - Journal of Physics: Conference Series
JF - Journal of Physics: Conference Series
SN - 1742-6588
IS - 1
M1 - 012114
ER -
ID: 9700099