Skip to main content
SpringerLink
Log in
Book cover

The Navier-Stokes Equations II — Theory and Numerical Methods pp 1–16Cite as

Analyticity of a free boundary in plane quasi-steady flow of a liquid form subject to variable surface tension

  • Free Boundary Problems
  • Conference paper
  • First Online:

  • 1626 Accesses

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1530))

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Antanovskii, L.K. Complex representation of the solutions of the Navier-Stokes equations for a low Reynolds number. Dinamika Sploshnoi Sredy 51, 3–16 (1981)

    Google Scholar 

  2. Antanovskii, L.K. Stability of a liquid film equilibrium under the action of thermocapillary forces in quasisteady approximation. Zh. Prikl. Mekh. Tekh. Fiz. No.2, 47–53 (1990)

    Google Scholar 

  3. Antanovskii, L.K. Boundary integral equations in quasisteady problems of capillary fluid mechanics. Part 2: Application of the stress-stream function. Meccanica-J. Ital. Assoc. Theoret. Appl. Mech. 26(1), 59–65 (1991)

    ADS  Google Scholar 

  4. Antanovskii, L.K. Bianalytic stress-stream function in plane quasi-steady problems of capillary fluid mechanics. Sibirsk. Matem. Zh. 33(1), 3–15 (1992)

    MathSciNet  Google Scholar 

  5. Belonosov, S.M. & Chernous, K.A. Boundary-Value Problems for the Navier-Stokes Equations. Moscow: Nauka (1985)

    MATH  Google Scholar 

  6. Bemelmans, J. & Friedman, A. Analyticity for the Navier-Stokes equations governed by surface tension on the free boundary. J. Diff. Equat. 55(1), 135–150 (1984)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Clarke, N.S. Two-dimensional flow under gravity in a jet of viscous liquid. J. Fluid. Mech. 31(3), 481–500 (1968)

    Article  ADS  MATH  Google Scholar 

  8. Gakhov, F.D. Boundary-Value Problems. Oxford: Pergamon Press (1966)

    MATH  Google Scholar 

  9. Garabedian, P.R. Free boundary flows of viscous liquid. Comm. Pure Appl. Math. 19(4), 421–434 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  10. Gibbs, J.W. Collected Works, 1. New Haven: Yale University Press (1948)

    MATH  Google Scholar 

  11. Goluzin, G.M. Geometric Theory of Functions of Complex Variable. Providence, Rhode Island: Amer. Math. Soc. (1969)

    Google Scholar 

  12. Hopper, R.W. Plane Stokes flow driven by capillarity on a free surface. J. Fluid Mech. 213, 349–375 (1990)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. Kolosov, G.V. Application of the Complex Variable to the Theory of Elasticity. Moscow-Leningrad: ONTI (1935)

    Google Scholar 

  14. Kuiken, H.K. Viscous sintering: the surface-tension-driven flow of a liquid form under the influence of curvature gradients at its surface. J. Fluid Mech. 214, 503–515 (1990)

    Article  ADS  MATH  Google Scholar 

  15. Martin, R.H.Jr. Nonlinear Operators and Differential Equations in Banach Spaces. Interscience, Wiley (1976)

    Google Scholar 

  16. Muskhelishvili, N.I. Some Basic Problems of Mathematical Theory of Elasticity. Groningen-Holland: Noordhoff (1953)

    MATH  Google Scholar 

  17. Ovsiannikov, L.V. A nonlinear Cauchy problem in a scale of Banach spaces. Dokl. Akad. Nauk SSSR 200(4), 789–792 (1971)

    MathSciNet  Google Scholar 

  18. Pukhnachov, V.V. On smoothness of the steady-state solutions of the Navier-Stokes equations near the free boundary. Dinamika Sploshnoi Sredy 15, 133–144 (1973)

    Google Scholar 

  19. Richardson, S. Two-dimensional bubbles in slow viscous flows. J. Fluid Mech. 33, 476–493 (1968)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Richardson, S. Two-dimensional bubbles in slow viscous flows. Part 2. J. Fluid Mech. 58, 115–127 (1973)

    Article  ADS  MATH  Google Scholar 

  21. Solonnikov, V.A. Unsteady motion of a finite mass of fluid, bounded by a free surface. Zap. Naucn. Sem. LOMI 152, 137–157 (1986)

    MATH  Google Scholar 

  22. Solonnikov, V.A. On the evolution of an isolated volume of a viscous incompressible capillary liquid for large values of time. Vestnik LGU. Ser. 1, No. 3, 49–55 (1987)

    Google Scholar 

Download references

Author information

Author notes

  1. Lenoid K. Antanovskii

    Present address: Microgravity Advanced Research and Support center, Via Diocleziano 328, 80125, Naples, Italy

Authors and Affiliations

  1. Lavrentyev Institute of Hydrodynamics, 630090, Novosibirsk, Russia

    Lenoid K. Antanovskii

Authors
  1. Lenoid K. Antanovskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

John G. Heywood Kyûya Masuda Reimund Rautmann Vsevolod A. Solonnikov

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag

About this paper

Cite this paper

Antanovskii, L.K. (1992). Analyticity of a free boundary in plane quasi-steady flow of a liquid form subject to variable surface tension. In: Heywood, J.G., Masuda, K., Rautmann, R., Solonnikov, V.A. (eds) The Navier-Stokes Equations II — Theory and Numerical Methods. Lecture Notes in Mathematics, vol 1530. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090330

Download citation

  • DOI: https://doi.org/10.1007/BFb0090330

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56261-0

  • Online ISBN: 978-3-540-47498-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation