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J. Sib. Fed. Univ. Math. Phys., 2011, Volume 4, Issue 3, Pages 320–331 (Mi jsfu190)  

This article is cited in 8 scientific papers (total in 8 papers)

Solution of two dual problems of gluing vorter and potential flows by M. A. Goldshtick variational method

Isaak I. Vainshtein

Institute of Space and Information Technologies, Siberian Federal University, Krasnoyarsk, Russia

Abstract: A general problem of motion of incompressible liquid with vortex zones with different constant vorticity is formulated. It is considered the M. A. Goldshtic variational method of the research of dual problems for flows with vortex and potential areas that describe the model of separated flows and the model of ideal liquid motion in a field of Coriolis forces. It is proved the existence of the second nontrivial solution to the M. A. Goldshtick problem.

Keywords: vortex and potential flows, variational method, Green's function, extremum of the functional.

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UDC: 517.55
Received: 18.01.2011
Received in revised form: 25.02.2011
Accepted: 10.03.2011

Citation: Isaak I. Vainshtein, “Solution of two dual problems of gluing vorter and potential flows by M. A. Goldshtick variational method”, J. Sib. Fed. Univ. Math. Phys., 4:3 (2011), 320–331

Citation in format AMSBIB
\by Isaak~I.~Vainshtein
\paper Solution of two dual problems of gluing vorter and potential flows by M.\,A.~Goldshtick variational method
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2011
\vol 4
\issue 3
\pages 320--331

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    This publication is cited in the following articles:
    1. D. K. Potapov, “O kolichestve reshenii v zadachakh na sobstvennye znacheniya dlya uravnenii ellipticheskogo tipa s razryvnymi nelineinostyami”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(26) (2012), 251–255  mathnet  crossref
    2. Dmitrii K. Potapov, “Zadachi upravleniya dlya uravnenii so spektralnym parametrom i razryvnym operatorom pri nalichii vozmuschenii”, Zhurn. SFU. Ser. Matem. i fiz., 5:2 (2012), 239–245  mathnet
    3. D. K. Potapov, “O chisle reshenii dlya odnogo klassa uravnenii ellipticheskogo tipa so spektralnym parametrom i razryvnoi nelineinostyu”, Dalnevost. matem. zhurn., 12:1 (2012), 86–88  mathnet
    4. Isaak I. Vainshtein, Irina M. Fedotova, “Dualnaya zadacha k zadache M. A. Goldshtika s neogranichennoi zavikhrennostyu”, Zhurn. SFU. Ser. Matem. i fiz., 5:4 (2012), 515–526  mathnet
    5. D. K. Potapov, “On solutions of the Gol'dshtik problem”, Num. Anal. Appl., 5:4 (2012), 342–347  mathnet  crossref  elib
    6. A. V. Vasin, “Opredelenie linii razdela oblastei vikhrevykh techenii”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 2013, no. 1, 3–10  mathnet
    7. Vasin A.V., Timofeeva O.A., “Modelirovanie zon vikhrevykh techenii v obvodnykh galereyakh shlyuzovykh kamer”, Gidrotekhnicheskoe stroitelstvo, 2013, no. 2, 17–21  mathscinet  elib
    8. Isaac I. Vainshtein, “Model problems for two nonlinear equations that type depends on the solution”, Zhurn. SFU. Ser. Matem. i fiz., 6:4 (2013), 539–547  mathnet
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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