Geodesic
Symmetry analysis of ideal fluid equations in terms of trajectories and Weber's potential
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 2, pp. 133-144

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: symmetry analysis
Mots-clés : Euler equations, Weber's transformation, equivalence transformation, group classification. 
@article{JSFU_2019_12_2_a0,
     author = {Victor K. Andreev and Daria A. Krasnova},
     title = {Symmetry analysis of ideal fluid equations in terms of trajectories and {Weber's} potential},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {133--144},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2019_12_2_a0/}
}
TY  - JOUR
AU  - Victor K. Andreev
AU  - Daria A. Krasnova
TI  - Symmetry analysis of ideal fluid equations in terms of trajectories and Weber's potential
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2019
SP  - 133
EP  - 144
VL  - 12
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2019_12_2_a0/
LA  - en
ID  - JSFU_2019_12_2_a0
ER  - 
%0 Journal Article
%A Victor K. Andreev
%A Daria A. Krasnova
%T Symmetry analysis of ideal fluid equations in terms of trajectories and Weber's potential
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2019
%P 133-144
%V 12
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2019_12_2_a0/
%G en
%F JSFU_2019_12_2_a0
Victor K. Andreev; Daria A. Krasnova. Symmetry analysis of ideal fluid equations in terms of trajectories and Weber's potential. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 2, pp. 133-144. http://geodesic.mathdoc.fr/item/JSFU_2019_12_2_a0/