A two-dimensional flow problem for steady-state Euler equations
Sbornik. Mathematics, Tome 66 (1990) no. 2, pp. 363-382
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A boundary value problem for plane and spatial axially symmetric flows of an ideal (inviscid and incompressible) fluid in a bounded domain is considered. Bibliography: 35 titles.
@article{SM_1990_66_2_a3,
     author = {O. V. Troshkin},
     title = {A two-dimensional flow problem for steady-state {Euler} equations},
     journal = {Sbornik. Mathematics},
     pages = {363--382},
     year = {1990},
     volume = {66},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1990_66_2_a3/}
}
TY  - JOUR
AU  - O. V. Troshkin
TI  - A two-dimensional flow problem for steady-state Euler equations
JO  - Sbornik. Mathematics
PY  - 1990
SP  - 363
EP  - 382
VL  - 66
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1990_66_2_a3/
LA  - en
ID  - SM_1990_66_2_a3
ER  - 
%0 Journal Article
%A O. V. Troshkin
%T A two-dimensional flow problem for steady-state Euler equations
%J Sbornik. Mathematics
%D 1990
%P 363-382
%V 66
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1990_66_2_a3/
%G en
%F SM_1990_66_2_a3
O. V. Troshkin. A two-dimensional flow problem for steady-state Euler equations. Sbornik. Mathematics, Tome 66 (1990) no. 2, pp. 363-382. http://geodesic.mathdoc.fr/item/SM_1990_66_2_a3/

[1] Agmon S, Duglas A., Nirenberg L., Otsenki reshenii ellipticheskikh uravnenii vblizi granitsy, IL, M., 1962

[2] Alekseev G. V., “O edinstvennosti i gladkosti ploskikh vikhrevykh techenii idealnoi zhidkosti”, Dinamika sploshnoi sredy (sb. nauchn. trudov), 15, Novosibirsk, 1973, 7–17 | MR

[3] Arnold V. I., Dopolnitelnye glavy teorii obyknovennykh differentsialnykh uravnenii, Nauka, M., 1978 | MR

[4] Bernshtein S. N., Sobr. soch., t. 3, AN SSSR, M., 1960

[5] Birman M. Sh., Skvortsov G. E., “O kvadratichnoi summiruemosti starshikh proizvodnykh resheniya zadachi Dirikhle v oblasti s kusochno gladkoi granitsei”, Izv. vuzov. Matematika, 1962, no. 5(30), 12–21 | MR | Zbl

[6] Bitsadze A. V., Nekotorye klassy uravnenii v chastnykh proizvodnykh, Nauka, M., 1981 | MR

[7] Vekua I. N., Obobschennye analiticheskie funktsii, Fizmatgiz, M., 1959 | MR

[8] Dezin A. A., “Nekotorye modeli, svyazannye s uravneniyami Eilera”, Differentsialnye uravneniya, 6:1 (1970), 17–26 | MR | Zbl

[9] Dezin A. A., Ob odnom klasse vektornykh polei, Kompleksnyi analiz i ego prilozheniya, Nauka, M., 1978 | MR

[10] Dezin A. A., Obschie voprosy teorii granichnykh zadach, Nauka, M., 1980 | MR | Zbl

[11] Dezin A. A., “Invariantnye formy i nekotorye strukturnye svoistva gidrodinamicheskikh uravnenii Eilera”, Zeit. Anal. Anwen., 2(5) (1983), 401–409 | MR | Zbl

[12] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz v normirovannykh prostranstvakh, Fizmatgiz, M., 1959 | MR

[13] Kochin N. E., Kibel I. A., Roze N. V., Teoreticheskaya gidromekhanika, Fizmatgiz, M., 1963 | Zbl

[14] Lavrentev M. A., Shabat B. V., Metody teorii funktsii kompleksnogo peremennogo, Nauka, M., 1973 | MR

[15] Lavrentev M. A., Shabat B. V., Problemy gidrodinamiki i ikh matematicheskie modeli, Nauka, M., 1977 | MR

[16] Lamb G., Gidrodinamika, Gostekhizdat, M., 1947

[17] Landis E. M., Uravneniya vtorogo poryadka ellipticheskogo i parabolicheskogo tipov, Nauka, M., 1971 | MR

[18] Mikhailov V. P., Differentsialnye uravneniya v chastnykh proizvodnykh, Nauka, M., 1976 | MR | Zbl

[19] Sobolev S. L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, LGU, L., 1950

[20] Troshkin O. V., “O nekotorykh svoistvakh eilerovskikh polei”, Differents. uravneniya, 18:1 (1982), 138–144 | MR | Zbl

[21] Troshkin O. V., “Dopustimost mnozhestva granichnykh znachenii v odnoi statsionarnoi gidrodinamicheskoi zadache”, DAN SSSR, 272:5 (1983), 1086–1090 | MR | Zbl

[22] Troshkin O. V., K kachestvennoi teorii sistem kvazilineinykh uravnenii s chastnymi proizvodnymi pervogo poryadka, Dis. ... kand. fiz.-matem. nauk, VTs AN SSSR, M., 1985

[23] Ekland I., Temam R., Vypuklyi analiz i variatsionnye problemy, Mir, M., 1979 | MR

[24] Yudovich V. I., “Dvumernaya nestatsionarnaya zadacha protekaniya idealnoi zhidkosti cherez zadannuyu oblast”, Matem. sb., 64(106) (1964), 562–588

[25] Dolph C. L., “Non-linear integral equations of the Hammerstein type”, Proc. Nat. Acad. Sci. U.S.A., 31 (1945), 60–65 | DOI | MR

[26] Dolph C. L., “Nonlinear integral equations of the Hammerstein tupe”, Trans. Amer. Math. Soc., 66:2 (1949), 289–307 | DOI | MR | Zbl

[27] Fraenkel L. E., “On corner eddies in plane inviscid shear flow”, J. Fluid Mech., 11:3 (1961), 400–406 | DOI | MR | Zbl

[28] Fraenkel L. E. Berger M. S., “A global theory of steady vortex rings in an ideal fluid”, Acta Math., 132:1 (1974), 13–51 | DOI | MR | Zbl

[29] Kato T., “On classical solutions of the two dimensional nonstationary Euler equation”, Arch. R. M. An., 25(3) (1967), 188–200 | MR | Zbl

[30] Landesman E. M., Lazer A. C., “Linear eigenvalues and a nonlinear boundary value problem”, Pacific J. Math., 33:2 (1970), 311–328 | MR | Zbl

[31] Lazer A. C, Landesman E. M., Meyers David R., “On Saddle Point Problems in the Calculus of Variations, the Ritz Algorithm and Monotone Convergence”, J. Math. Anal. Appl., 52:3 (1975), 594–614 | DOI | MR | Zbl

[32] Wigley N. M., “Asymptotic Expansions at a Corner of Solutions of Mixed Boundary Value Problems”, J. Math. Mech., 13:4 (1964), 549–576 | MR | Zbl

[33] Wigley N. M., “Development of the Mapping function at a corner”, Pac. J. Math., 15:4 (1965), 1435–1461 | MR | Zbl

[34] Wigley N. M., “Mixed Boundary Value Problems in Plane Domains with Corners”, Math. Z., 115:1 (1970), 33–52 | DOI | MR | Zbl

[35] Wolibner W., “On theoreme sur l'existence du mouvement plan d'un fluide parfait, homogene, incompressible, pendant un temps infiniment longue”, Math. Z., 37 (1933), 698–726 | DOI | MR | Zbl