Geodesic
The dual problem to M.\,A.~Ggoldshtik problem with unbounded vorticity
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 4, pp. 515-526.

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The existence and uniqueness of solutions of the dual problem to M. A. Goldshtik problem with unbounded increasing from the flow function vorticity. The solutions in the explicit form was determined on a model example for Liouville equation.
Keywords: vortex and potential flows, integral equation, Green function
Mots-clés : Liouville equation. 
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Isaak I. Vainshtein; Irina M. Fedotova. The dual problem to M.\,A.~Ggoldshtik problem with unbounded vorticity. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 4, pp. 515-526. http://geodesic.mathdoc.fr/item/JSFU_2012_5_4_a8/

[1] I. I. Vainshtein, “Dualnaya zadacha k zadache M. A. Goldshtika s proizvolnoi zavikhrennostyu”, Zhurnal Sibirskogo federalnogo universiteta. Matematika i fizika, 3:4 (2010), 500–506

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

[3] I. I. Vainshtein, “Reshenie dvukh dualnykh zadach o skleike vikhrevykh i potentsialnykh techenii variatsionnym metodom M. A. Goldshtika”, Zhurnal Sibirskogo federalnogo universiteta. Matematika i fizika, 4:3 (2011), 320–331

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

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

[6] I. I. Privalov, Subgarmonicheskie funktsii, ONTI, M., 1937

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