Geodesic
Method of successive approximations for the problem of fluid flow in a deformable domain
Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 1, pp. 33-52 
A. B. Morgulis. Method of successive approximations for the problem of fluid flow in a deformable domain. Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 1, pp. 33-52. http://geodesic.mathdoc.fr/item/VMJ_2010_12_1_a3/
@article{VMJ_2010_12_1_a3,
     author = {A. B. Morgulis},
     title = {Method of successive approximations for the problem of fluid flow in a deformable domain},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {33--52},
     year = {2010},
     volume = {12},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2010_12_1_a3/}
}
TY  - JOUR
AU  - A. B. Morgulis
TI  - Method of successive approximations for the problem of fluid flow in a deformable domain
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2010
SP  - 33
EP  - 52
VL  - 12
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VMJ_2010_12_1_a3/
LA  - ru
ID  - VMJ_2010_12_1_a3
ER  - 
%0 Journal Article
%A A. B. Morgulis
%T Method of successive approximations for the problem of fluid flow in a deformable domain
%J Vladikavkazskij matematičeskij žurnal
%D 2010
%P 33-52
%V 12
%N 1
%U http://geodesic.mathdoc.fr/item/VMJ_2010_12_1_a3/
%G ru
%F VMJ_2010_12_1_a3

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

We justify an iterative procedure for the solving of the general initial-boundary value problem of the inviscid fluid dynamics in the case of deformable flow domain. Using this approach we prove the existence and uniqueness of the solution.

[1] Pedli T., Gidrodinamika krupnykh krovenosnykh sosudov, Mir, M., 1983, 400 pp.

[2] Sennitskii V. L., “O povedenii pulsiruyuschego tverdogo tela v vyazkoi zhidkosti v prisutstvii sily tyazhesti”, PMTF, 42:5 (2001), 93–97 | Zbl

[3] Miloh T., Galper A., “Self-propulsion of general deformable shapes in a perfect fluid”, Proc. Roy. Soc. London A, 442 (1993), 273–299 | DOI | Zbl

[4] Yudovich V. I., “Nestatsionarnye techeniya idealnoi neszhimaemoi zhidkosti”, Zhurn. vychisl. mat-ki i mat. fiziki, 3:6 (1963), 1032–1066 | MR | Zbl

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

[6] Yudovich V. I., “Dvumernaya nestatsionarnaya zadacha o protekanii idealnoi neszhimaemoi zhidkosti cherez zadannuyu oblast”, Mat. sb., 64:4 (1964), 562–588 | MR

[7] Polia G., Segë G., Izoperimetricheskie neravenstva v matematicheskoi fizike, Fizmatgiz, M., 1962, 336 pp. | MR

[8] Yudovich V. I., “Nekotorye otsenki reshenii ellipticheskikh uravnenii”, Mat. sb., 59:101 (1962), 229–244 | MR | Zbl

[9] Gilbarg D., Trudinger N., Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989, 464 pp. | MR | Zbl

[10] Stein I., Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973, 344 pp. | MR

[11] Yudovich V. I., Metod linearizatsii v gidrodinamicheskoi teorii ustoichivosti, Izd-vo RGU, Rostov-na-Donu, 1984, 180 pp. | Zbl

[12] Khartman F., Obyknovennye differentsialnye uravneniya, Mir, M., 1970, 720 pp. | MR

[13] Yudovich V. I., “Uniqueness theorem for the basic nonstationary problem in the dynamics of an ideal incompressible fluid”, Math. Res. Lett., 2:1 (1995), 27–38 | DOI | MR | Zbl

[14] Vishik M., “Incompressible flows of an ideal fluid with vorticity in borderline spaces of Besov type”, Ann. Sci. Ecole Norm. Sup. (4), 32:6 (1999), 769–812 | MR | Zbl