Symmetry Analysis of Ideal Fluid Equations in Terms of Trajectories and Weber’s Potential
Andreev, V. K.
Krasnova, D. A.
Институт математики и фундаментальной информатики
Базовая кафедра математического моделирования и процессов управления
Journal Name:Journal of Siberian Federal University - Mathematics and Physics
Journal Quartile in Scopus:Q3
Journal Quartile in Web of Science:без квартиля
Bibliographic Citation:Andreev, V. K. Symmetry Analysis of Ideal Fluid Equations in Terms of Trajectories and Weber’s Potential [Текст] / V. K. Andreev, D. A. Krasnova // Journal of Siberian Federal University - Mathematics and Physics. — 2019. — Т. 12 (№ 2). — С. 133-144
The 2D perfect ﬂuid motions equations in Lagrangian coordinates are considered. If body forces are potential one, then there is the general integral called Weber’s integral and the resulting system includes initial data which in fact make the problem of group-theoretical classiﬁcation actual. It is established that the basic group becomes inﬁnite-dimensional with respect to the space variable too. The exceptional values of arbitrary initial vorticity are obtained at which we can be observed further extension of the group. Group properties of Euler equations in arbitrary Lagrangian coordinates are also considered and some exact solutions are constructed.