Geodesic
The dual problem to M.\,A.~Goldshtik problem with arbitrary vorticity
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 3 (2010) no. 4, pp. 500-506.

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The existence of solutions of the dual problem to M. A. Goldshtik problem with arbitrary vorticity was proved in this paper. The effect of non-uniqueness of the solution was determined on a model example.
Keywords: vortex and potential flows, integral equation, Green function
Mots-clés : Liouville equation. 
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Isaak I. Vainshtein. The dual problem to M.\,A.~Goldshtik problem with arbitrary vorticity. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 3 (2010) no. 4, pp. 500-506. http://geodesic.mathdoc.fr/item/JSFU_2010_3_4_a6/

[1] M. A Goldshtik, “Matematicheskaya model otryvnykh techenii neszhimaemoi zhidkosti”, Dokl. AN SSSR, 8:6 (1962), 1310–1313

[2] I. I. Vainshtein, M. A. Goldshtik, “O dvizhenii idealnoi zhidkosti v pole koriolisovykh sil”, Dokl. AN SSSR, 6:6 (1967), 1277–1230

[3] I. I. Vainshtein, O dvizhenii idealnoi zhidkosti s zavikhrennymi zonami, Avtoreferat dissertatsii na soiskanie uchenoi stepeni kandidata fiziko-matematicheskikh nauk, Novosibirsk, 1972, 12 pp.

[4] M. A Goldshtik, Vikhrevye potoki, Nauka, Novosibirsk, 1961

[5] I. I. Vainshtein, V. K. Yurovskii, “Ob odnoi zadache sopryazheniya vikhrevykh i potentsialnykh techenii idealnoi zhidkosti”, Zh. prikl. mekh. i tekhn. fiz., 1976, no. 6, 98–100

[6] I. I. Vainshtein, P. S. Litvinov, “Model M. A. Lavrenteva o skleike vikhrevykh i potentsialnykh techenii idealnoi zhidkosti”, Vestnik SibGAU, 24:3 (2009), 7–9 | MR

[7] P. S. Litvinov, Matematicheskoe modelirovanie dvukhsloinykh potokov v podshipnikakh skolzheniya, separatorakh i techeniyakh po skheme M. A. Lavrenteva, Avtoreferat dissertatsii na soiskanie uchenoi stepeni kandidata fiziko-matematicheskikh nauk, Krasnoyarsk, 2009, 24 pp.

[8] M. G. Lepchinskii, Suschestvovanie i ustoichivost kraevykh zadach s razryvnymi nelineinostyami, Avtoreferat dissertatsii na soiskanie uchenoi stepeni kandidata fiziko-matematicheskikh nauk, Ekaterinburg, 2008, 24 pp.

[9] A. B. Shabat, “O dvukh zadachakh na skleivanie”, Dokl. AN SSSR, 150:6 (1963), 1242–1245 | MR

[10] S. N. Antontsev, V. D. Lelyukh, Dinamika sploshnoi sredy, 1, 1969, 131–153

[11] P. I. Plotnikov, “O razreshimosti odnogo klassa zadach na skleivanie vikhrevykh i potentsialnykh techenii”, Dinamika sploshnoi sredy, 3, 1969, 61–69

[12] R. Kurant, Uravneniya s chastnymi proizvodnymi, Nauka, M., 1964 | MR

[13] E. I. Semenov, “O novykh tochnykh resheniyakh neavtonomnogo uravneniya Liuvillya”, Sib. matem. zhurn., 49:1 (2008), 207–217 | MR | Zbl