Siberian Mathematical Journal

, Volume 33, Issue 1, pp 1–11 | Cite as

Bianalytic stress-flow function in plane quasistationary problems of capillary hydrodynamics

  • L. K. Antanovskii


Quasistationary Problem Capillary Hydrodynamic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    M. A. Lavrent'ev and B. V. Shabat, Methods of the Theory of Functions of the Complex Variable [in Russian], Nauka, Moscow (1973).Google Scholar
  2. 2.
    L. M. Miln-Thomson, Theoretical Hydrodynamics [Russian translation], Mir, Moscow (1964).Google Scholar
  3. 3.
    G. V. Kolosov, Application of the Complex Variable to the Theory of Elasticity [in Russian], ONTI, Moscow-Leningrad (1935).Google Scholar
  4. 4.
    N. I. Muskhelishvili, Some Fundamental Problems of Mathematical Theory of Elasticity [in Russian], Izd. Akad. Nauk SSSR, Moscow (1954).Google Scholar
  5. 5.
    V. S. Vinogradov, “A new method of solutions of the boundary problem for a linearized system of Navier-Stokers equations in the two-dimensional case,” Dokl. Akad. Nauk SSSR,145, No. 6, 1202–1204 (1962).Google Scholar
  6. 6.
    D. G. Ionescu, “La méthode des fonctions analytique dans l'hydrodynamique des liquides visqueux,” Rev. Méc. Appl.,8, No. 4, 675–709 (1963).Google Scholar
  7. 7.
    A. V. Bitsadze, Some Classes of Partial Differential Equations [in Russian], Nauka, Moscow (1981).Google Scholar
  8. 8.
    S. M. Belonosov and K. A. Chernous, Boundary Problems for Navier-Stokes Equations [in Russian], Nauka, Moscow (1985).Google Scholar
  9. 9.
    C. J. Coleman, “A contour integral formulation of plane creeping Newtonian flow,” Q. J. Mech. Appl. Math.,34, 453–464 (1981).Google Scholar
  10. 10.
    N. S. Clarke, “Two-dimensional flow under gravity in a jet of viscous liquid,” J. Fluid Mech.,31, 481–500 (1968).Google Scholar
  11. 11.
    P. R. Garabedian, “Free boundary flows of viscous liquid,” Commun. Pure Appl. Math.,19, No. 4, 421–434 (1966).Google Scholar
  12. 12.
    S. Richardson, “Two-dimensional bubbles in slow viscous flows,” J. Fluid Mech.,33, 476–493 (1969).Google Scholar
  13. 13.
    S. Richardson, “Two-dimensional bubbles in slow viscous flows. Part 2,” J. Mech.,58, 115–127 (1973).Google Scholar
  14. 14.
    L. K. Antanovskii, “Complex representation of solutions of Navier-Stokes equations,” Dokl. Akad. Nauk SSSR,261 No. 4, 829–832 (1981).Google Scholar
  15. 15.
    L. K. Antanovskii, “Exact solutions of the free boundary problem for Stokes system,” Dokl. Akad. Nauk SSSR,270, No. 5, 1082–1084 (1983).Google Scholar
  16. 16.
    L. K. Antanovskii, “Boundary value problems with free boundaries for the Stokes systems on a plane,” Dokl. Akad. Nauk SSSR,290, No. 3, 586–590 (1986).Google Scholar
  17. 17.
    L. K. Antanovskii, Methods of the Theory of Functions of the Complex Variable Applied to Hydrodynamics of Viscous Liquid with Free Boundaries [in Russian], Dep. VINITI 28.03.86, No. 2161-B, Novosibirsk (1986).Google Scholar
  18. 18.
    L. K. Antanovskii, “Dynamics of the interphase boundary under the action of capillary forces. Quasistationary plane-parallel motion,” Prikl. Mat. Teor. Fiz., No. 3, 90–94 (1988).Google Scholar
  19. 19.
    L. K. Antanovskii, “Modeling problem of filling a plane cylinder with viscous liquid,” Dinam. Sploshn. Sredy,93–94 3–8 (1989).Google Scholar
  20. 20.
    L. K. Antanovskii, “Stability of equilibrium of a layer of liquid under the action of thermocapillary forces in quasistationary approximation,” Prikl. Mat. Teor. Fiz., No. 2, 47–53 (1990).Google Scholar
  21. 21.
    R. W. Hopper, “Plane Stokes flow driven by capillarity on a free surface,” J. Fluid Mech.,213, 349–375 (1990).Google Scholar
  22. 22.
    L. G. Napolitano, “Thermodynamics and dynamics of pure interfaces,” Acta Astronaut.,5, No. 9, 655–670 (1978).Google Scholar
  23. 23.
    E. B. Dussan and S. H. Davis, “On the motion of a fluid-fluid interface along a solid surface,” J. Fluid Mech.,65, 73–97 (1974).Google Scholar
  24. 24.
    V. A. Solonnikov, “Solvability of the problem of the plane motion of a heavy viscous incompressible capillary liquid that partialy fills a certain vessel,” Izv. Akad. Nauk SSSR, Ser. Mat.,43, No. 1, 203–236 (1979).Google Scholar
  25. 25.
    F. D. Gakhov, Boundary Problems [in Russian], Nauka, Moscow (1977).Google Scholar
  26. 26.
    S. G. Krein and G. I. Laptev, “On the problem of flow of a viscous liquid in an open container,” Funkts. Anal. Prilozh.,2, No. 1, 40–50 (1968).Google Scholar
  27. 27.
    G. I. Éskin, Boundary Problems for Elliptic Pseudo-Differential Equations [in Russian], Nauka, Moscow (1973).Google Scholar
  28. 28.
    I. N. Vekua, Generalized Analytic Functions [in Russian], Nauka, Moscow (1988).Google Scholar
  29. 29.
    N. I. Muskhelishvili, Singular Integral Equations [in Russian], Nauka, Moscow (1968).Google Scholar
  30. 30.
    G. M. Goluzin, Geometrical Theory of Functions of the Complex Variable [in Russian], Nauka, Moscow (1966).Google Scholar
  31. 31.
    V. I. Nalimov, “New model of the Cauchy-Poisson problem,” Dinam. Sploshn. Sredy,12, 86–123 (1972).Google Scholar
  32. 32.
    D. Henry, Geometrical Theory of Semi-Linear Parabolic Equations [Russian translation], Mir, Moscow (1985).Google Scholar
  33. 33.
    V. A. Solonnikov, “Unsteady flow of a finite mass of a fluid bounded by a free surface,” Zap. Nauch. Sem. LOMI, Akad. Nauk SSSR,152, 137–157 (1986).Google Scholar
  34. 34.
    V. A. Solonnikov, “On evolution of an isolated volume of viscous incompressible capillary liquid for large values of time,” Vestn. Lenin. Univ., Ser. 1, Math. Mech., Astron.,3, 49–55 (1987).Google Scholar

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • L. K. Antanovskii

There are no affiliations available

Personalised recommendations