Skip to main content
SpringerLink
Log in

L q-Estimates for a Solution to the Problem about the Evolution of an Isolated Amount of a Fluid

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

We construct the L q-theory of the nonstationary free boundary problem for the Navier–Stokes equations under the action of surface tension forces. Although the main theorem is proved for some finite time interval, it can be used for extending the solution to a larger interval since the smoothness of the solution is preserved for t < 0. Bibliography: 10 titles.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. A. Solonnikov, “Solvability of the problem of evolution of an isolated amount of a viscous incompressible capillary fluid,” Zap. Nauchn. Semin. LOMI [in Russian], 140, 179–186(1984)

    Google Scholar 

  2. V. A. Solonnikov, “Solvability of a problem on the evolution of a viscous incompressible fluid, bounded by a free surface, on a finite time interal” [in Russian], Algebra Anal [in Russian], 3, 222–257(1991); English transl.: St. Petersburg Math. J., 3, No. 11, 189–220 (1992)

    Google Scholar 

  3. I. Sh. Mogilevskii and V. A. Solonnikov, “On the solvability of an evolution free boundary problem for the Navier–Stokes equations in the H¨ older spaces of functions,” Mathematical Problems Related to the Navier–Stokes Equations. Series on Advances in Mathematics for Applied Sciences, 11, 105–181(1992)

    Google Scholar 

  4. V. A. Solonnikov, “On the justification of the quasistationary approximation in the problem of motion of aviscous capillary drop,” Interfaces and Free Boundaries, 1, 125–173(1999)

    Google Scholar 

  5. V. A. Solonnikov, “Lectures on Evolution Free Boundary Problems: Classical Solutions,” Lect. Notes Math.[to appear]

  6. V. A. Solonnikov, “Estimates of the solution of a certain initial-boundaryvalue problem,” Zap. Nauchn. Semin. LOMI [in Russian], 59, 178–254(1976)

    Google Scholar 

  7. I. Sh. Mogilevskii, “Estimates for solutions to the general initial-boundary value problem for a linear non-stationary Navier–Stokes equations in a half-space,” Zap. Nauchn. Semin. LOMI[in Russian], 84, 147–173(1979)

    Google Scholar 

  8. K. K. Golovkin, “On some smoothness conditions for functions of several variables and on estimates for the convolution operators,” Dokl. Akad. Nauk SSSR [in Russian], 139, 524–527(1961)

    Google Scholar 

  9. I. Sh. Mogilevskii and V. A. Solonnikov, “The solvability of a noncoercive initial-boundary value problem for the Stokes system in H¨ olderl classes of functions (the case of a half-space),” Zeitschriftt fur Analysis und ihre Anwendungen, 8, 329–347, (1989)

    Google Scholar 

  10. V. A. Solonnikov, “Unsteady flow of a finite mass of a fluid bounded by a free surface,” Zap. Nauchn. Semin. LOMI [in Russian], 152, 137–157(1986)

    Google Scholar 

Download references

Authors
  1. V.A. Solonnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Solonnikov, V. L q-Estimates for a Solution to the Problem about the Evolution of an Isolated Amount of a Fluid. Journal of Mathematical Sciences 117, 4237–4259 (2003). https://doi.org/10.1023/A:1024872705127

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1024872705127

Keywords

Search

Navigation