Geodesic
Submodels in gas dynamics with linear field of velocity
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 9 (2012), pp. 208-226.

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

We consider the gas dynamics equation with an arbitrary state equation. After substitution of solution in the form of the linear field of velocity in equation of gas dynamics, the set of equations is received. Research of its compatibility gives a terminating parity into which the auxiliary matrix enters. This parity allowed to make classification of all submodels by a rank of an auxiliary matrix. All submodels for zero, degenerate and nondegenerate auxiliary matrixes are found. In separate point the case when the density depends only on time is considered. Quite certain submodel is found. It is as a result received quite certain 11 submodels of flow of gas with the linear field of velocity. For each submodel the equation of state is found.
Keywords: gas dynamics, line field of velocity, submodel. 
@article{SEMR_2012_9_a24,
     author = {Yu. V. Yulmukhametova},
     title = {Submodels in gas dynamics with linear field of velocity},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {208--226},
     publisher = {mathdoc},
     volume = {9},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2012_9_a24/}
}
TY  - JOUR
AU  - Yu. V. Yulmukhametova
TI  - Submodels in gas dynamics with linear field of velocity
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2012
SP  - 208
EP  - 226
VL  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2012_9_a24/
LA  - ru
ID  - SEMR_2012_9_a24
ER  - 
%0 Journal Article
%A Yu. V. Yulmukhametova
%T Submodels in gas dynamics with linear field of velocity
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2012
%P 208-226
%V 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2012_9_a24/
%G ru
%F SEMR_2012_9_a24
Yu. V. Yulmukhametova. Submodels in gas dynamics with linear field of velocity. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 9 (2012), pp. 208-226. http://geodesic.mathdoc.fr/item/SEMR_2012_9_a24/

[1] G. L. Dirichlet, “Untersuchunger uber eih Problem der Gydrodynamik”, J. Reine Angev. Math., 58 (1860), 181

[2] B. Riman, Sochineniya, GITTL, Moskva–Leningrad, 1948

[3] L.V. Ovsyannikov, “Novoe reshenie uravnenii gidrodinamiki”, Dokl. AN SSSR, 111(1) (1956), 47–49 | MR | Zbl

[4] J.F. Dyson, “Dynamics of a spinning gas cloud”, J. Math. Mech., 18(1) (1968), 91–101 | Zbl

[5] V.K. Andreev, “K zadache o neustanovivshemsya dvizhenii szhimaemoi zhidkosti so svobodnoi granitsei”, DAN SSSR, 244(5) (1979), 1107–1110 | MR | Zbl

[6] O.I. Bogoyavlenskii, Metody kachestvennoi teorii dinamicheskikh sistem v astrofizike i gazovoi dinamike, Nauka, Moskva, 1980 | MR

[7] I.V. Nemchinov, “Razlet trekhosnogo gazovogo ellipsoida v regulyarnom rezhime”, PMM, 29(1) (1965), 134–140

[8] S.I. Anisimov, Yu.I. Lysikov, “Razlet trekhosnogo gazovogo ellipsoida v regulyarnom rezhime”, PMM, 34(5) (1970), 926–929 | Zbl

[9] S.I. Anisimov, N.A. Inogamov, “Razvitie neustoichivosti i poterya simmetrii pri izentropicheskom szhatii sfericheskoi kapli”, Pisma v ZhETF, 20(3) (1974), 174–176

[10] S.V. Khabirov, “Dvizheniya gaza bez raskhozhdeniya s lineinym polem skorostei”, Trudy instituta matematiki s VTs UNTs RAN, 1 (2008), 208–215

[11] M. Fujimoto, “Gravitational collapse of rotating gaseous ellipsoids”, The Astrophysical Journal, 152 (1967), 523–536 | DOI

[12] L.Z. Urazbakhtina, Matematicheskoe modelirovanie dvizheniya szhimaemoi zhidkosti metodami gruppovogo analiza, dissertatsiya na soiskanie uchenoi stepeni kandidata fiziko-matematicheskikh nauk, 2009 | Zbl