Geodesic
Exact solutions of the transonic equations of gas dynamics
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 7 (2007) no. 1, pp. 54-63 
E. O. Kuznetsova; I. A. Chernov. Exact solutions of the transonic equations of gas dynamics. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 7 (2007) no. 1, pp. 54-63. http://geodesic.mathdoc.fr/item/ISU_2007_7_1_a10/
@article{ISU_2007_7_1_a10,
     author = {E. O. Kuznetsova and I. A. Chernov},
     title = {Exact solutions of the transonic equations of gas dynamics},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {54--63},
     year = {2007},
     volume = {7},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2007_7_1_a10/}
}
TY  - JOUR
AU  - E. O. Kuznetsova
AU  - I. A. Chernov
TI  - Exact solutions of the transonic equations of gas dynamics
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2007
SP  - 54
EP  - 63
VL  - 7
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ISU_2007_7_1_a10/
LA  - ru
ID  - ISU_2007_7_1_a10
ER  - 
%0 Journal Article
%A E. O. Kuznetsova
%A I. A. Chernov
%T Exact solutions of the transonic equations of gas dynamics
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2007
%P 54-63
%V 7
%N 1
%U http://geodesic.mathdoc.fr/item/ISU_2007_7_1_a10/
%G ru
%F ISU_2007_7_1_a10

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

The review exact (described by algebraic functions) solutions of a transonic set of Karman–Falkovitch equations is given. Self-similar solutions and two classes of the polynomial-parametrical solutions associated with self-similar at indexes $n=2$ and $n=3$ are considered. Connection with local exposition of singularities of transonic flows is specified, in particular in Laval nozzles.

[1] Falkovich S. V., Chernov I. A., “Obtekanie tela vrascheniya zvukovym potokom gaza”, Prikladnaya matematika i mekhanika, 28 (1964), 280–284 | MR

[2] Nemtsova E. O., Parametricheskii metod v izuchenii transzvukovykh uravnenii, Dep. v VINITI 26.07.05 No 1089-V2005, Saratov, 2005, 18 pp.

[3] Nemtsova E. O., “Parametricheskie resheniya transzvukovogo uravneniya i ikh svyaz s avtomodelnymi”, Materialy Chetvertoi molodezhnoi nauch. shkoly-konf., Tr. Matem. tsentra im. N. I. Lobachevskogo, 31, 2005, 110–113

[4] Chernov I. A., “Polinomo-parametricheskie resheniya transzvukovykh uravnenii”, Aerodinamika. Nelineinye problemy: Mezhvuz. sb. nauch. tr., 14(17), Izd-vo Sarat. un-ta, Saratov, 1997, 91–102

[5] Sevostyanov G. D., “Struktura elementarnykh okolozvukovykh reshenii”, Aerodinamika: Mezhvuz. sb. nauch. tr., 14(17), Izd-vo Sarat. un-ta, Saratov, 1997, 109–117

[6] Zaslavskii B. I., “O nelineinom vzaimodeistvii sfericheskoi udarnoi volny, voznikshei v rezultate vzryva zaglublennogo zaryada so svobodnoi poverkhnostyu vody”, Prikladnaya matematika i tekhnicheskaya fizika, 1964, no. 4, 57–65

[7] Zaslavskii B. I., Klepikova N. A., “Ob odnom klasse tochnykh chastnykh reshenii uravnenii okolozvukovykh techenii gaza”, Prikladnaya matematika i tekhnicheskaya fizika, 1965, no. 6, 65–68 | MR

[8] Kuznetsova E. O., “Model neraschetnogo rezhima techeniya v sople Lavalya”, Materialy Pyatoi molodezhnoi nauch. shkoly-konf., Tr. Matem. tsentra im. N. I. Lobachevskogo, 34, 2006, 136–139

[9] Ryzhov O. S., “O rabote sopel Lavalya v neraschetnykh rezhimakh”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 7:4 (1967) | Zbl