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

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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. 
@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},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2010_12_1_a3/}
}
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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/