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Solvability of a three-dimensional stationary flowing problem

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References

  1. N. E. Kochin, “On an existence theorem in hydrodynamics,” Prikl. Mat. Mekh.,20, No. 10, 5–28 (1957).

    Google Scholar 

  2. V. I. Yudovich, “A two-dimensional nonstationary problem of the flowing of an ideal incompressible fluid through a given domain,” Mat. Sb.,64, No. 4, 562–588 (1964).

    Google Scholar 

  3. M. R. Ukhovskiî, “On an axisymmetric initial boundary value problem for the equations of motion of an ideal incompressible fluid,” Mekhanika Zhidkosti Gaza, No.3, 3–12 (1967).

    Google Scholar 

  4. A. V. Kazhikhov, “A remark on the statement of the flowing problem for the equation of an ideal fluid,” Prikl. Mat. Mekh.,44, No. 5 (1980). 0111 0147 V 3

  5. V. Zayachkovski, “On local solvability of a flowing problem for an ideal incompressible fluid,” Zap. Nauch. Seminarov LOMI,96, Nauka, Leningrad, 1980, pp. 39–56.

    Google Scholar 

  6. M. R. Ukhovskiî, “On solvability of the three-dimensional flowing problem for an ideal incompressible fluid,” submitted to VINITI on March 27, 1979, No. 1051-79.

  7. S. N. Antontsev, A. V. Kazhikhov, and V. N. Monakhov, Boundary Value Problems of Inhomogeneous Fluid Mechanics [in Russian], Nauka, Novosibirsk (1983).

    Google Scholar 

  8. A. V. Kazhikhov, “Well-posedness of the problem of nonstationary flowing of an ideal fluid through a given domain,” Dinamika Sploshn. Sredy,47, 37–56 (1980).

    Google Scholar 

  9. V. M. Solopenko, “The solvability property of the nonsteady Euler equations in terms ofH and ψ,” Dokl. Akad. Nauk SSSR,305, No. 3, 567–571 (1989).

    Google Scholar 

  10. G. V. Alekseev, “On vanishing viscosity in the two-dimensional stationary problems of the hydrodynamics of an incompressible fluid,” Dinamika Sploshn. Sredy (Novosibirsk), No. 10, 5–28 (1972).

    Google Scholar 

  11. M. A. Gol'dshtik, Vortex Flows [in Russian], Nauka, Novosibirsk (1981).

    Google Scholar 

  12. A. Morgulis, V. Yudovich, and G. Zaslavsky, “Compressible helical flows,” Comm. Pure Appl. Math.,88, 571–582 (1995).

    Article  Google Scholar 

  13. G. V. Alekseev, “On uniqueness and smoothness of plane vortex flows of an ideal fluid,” Dinamika Sploshn. Sredy (Novosibirsk), No. 15, 7–18 (1973).

    Google Scholar 

  14. O. F. Vasil'ev, Foundations of Mechanics of Helical and Rotational Flows [in Russian], Gosènergo, Moscow and Leningrad (1958).

    Google Scholar 

  15. V. I. Arnol'd, Mathematical Methods in Classical Mechanics [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  16. G. M. Zaslavskiî, R. Z. Sagdeev, D. A. Usikov, and A. A. Chernikov, Weak Chaos and Quasiregular Structures [in Russian], Nauka, Moscow (1991).

    Google Scholar 

  17. S. Friedlander and M. M. Vishik, “Instability criteria for the flow of an inviscid incompressible fluid,” Phys. Rev. Let.,66, No. 17, 2204–2206 (1991). (see alsoS. Friedlander, M. M. Vishik, and A. Gilbert Hydrodynamic Instability and Certain ABC Flows [Preprint] (1993).)

    Article  MATH  Google Scholar 

  18. O. A. Oleînik and E. V. Radkevich, Second-Order Equations with Nonnegative Characteristic Form [in Russian], VINITI, Moscow (1971).

    Google Scholar 

  19. N. M. Gyunter, “On determination of velocity from vortex in the case of a liquid in a closed vessel,” Zh. Leningr. Fiz.-Mat. Obshch.,1, No. 1, 12–36 (1926).

    Google Scholar 

  20. S. G. Kreîn, “On the functional analytic properties of the operator of vector analysis and hydrodynamics,” Dokl. Akad. Nauk SSSR,93, No. 6, 969–972 (1953).

    Google Scholar 

  21. È. B. Bykhovskiî and N. V. Smirnov, “On the orthogonal decomposition of the space of vector-functions square-summable on a given domain and operators of vector analysis,” Trudy Mat. Inst. Steklov. Akad. Nauk SSSR, No. 59, 5–36 (1960).

    Google Scholar 

  22. N. D. Kopachevskiî, S. G. Kreîn, and Kan Zuî Ngo, Operator Methods in Linear Hydrodynamics: Evolution and Spectral Problems [in Russian], Nauka, Moscow (1989).

    Google Scholar 

  23. V. A. Solonnikov, “On overdetermined elliptic boundary value problems,” Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI),21, 112–158 (1971).

    Google Scholar 

  24. V. I. Yudovich, The Linearization Method in Hydrodynamic Stability Theory [in Russian], Rostovsk. Univ., Rostov-on-Don (1984).

    MATH  Google Scholar 

  25. D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order [Russian translation], Nauka, Moscow (1989).

    MATH  Google Scholar 

  26. C. Baiocchi and A. Capelo, Variational and Quasivariational Inequalities. Application to Free Boundary Problems [Russian translation], Nauka, Moscow (1988).

    Google Scholar 

  27. V. I. Yudovich, “Some estimates of solutions to elliptic equations,” Mat. Sb.,59, 229–244 (1962).

    Google Scholar 

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Authors
  1. A. B. Morgulis
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Additional information

The research was supported by the Competition Center for Basic Natural Sciences at St. Petersburg State University (Grant 95-0-2.1-115).

Rostov-on-Don. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 40, No. 1, pp. 142–158, January–February, 1999.

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Morgulis, A.B. Solvability of a three-dimensional stationary flowing problem. Sib Math J 40, 121–135 (1999). https://doi.org/10.1007/BF02674298

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