Skip to main content
SpringerLink
Log in

On the global unique solvability of some two-dimensional problems for the water solutions of polymers

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

Abstract

The global unique solvability of the two-dimensional initial-boundary-value problem with some slip-boundary conditions for a quasilinear system describing the flow of weak water solutions of polymers is proved. It is noted that the global unique solvability of the Cauchy problem and the initial-boundary-value problem with periodic boundary conditions are proved in a similar way. Biblography 14 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. L. I. Sedov,Continuum Mechanics [in Russian], Moscow (1970).

  2. L. S. Artushkov,Non-Newtonian Liquid Dynamics [in Russian], Leningrad (1979).

  3. A. P. Oskolkov, “Initial-boundary-value problem with a slip-boundary condition for the modified Navier-Stokes equations”,Zap. Nauchn. Semin. POMI,213, 93–115 (1994).

    Google Scholar 

  4. A. P. Oskolkov, “On the global solvability of the first boundary value problem for a third-order quasilinear system arising from the viscous liquid dynamics”,Zap. Nauchn. Semin. LOMI,27, 145–160 (1972).

    Google Scholar 

  5. A. P. Oskolkov, “On uniqueness and global solvability of boundary-value problems for equations describing the motion of the water solutions of polymers”,Zap. Nauchn. Semin. LOMI,38, 98–136 (1973).

    Google Scholar 

  6. A. P. Oskolkov, “On non-stationary flows of viscoewlastic liquids”,Trudy Mat. Inst. Akad. Nauk SSSR,159, 101–131 (1983).

    Google Scholar 

  7. O. A. Ladyzhenskaya,Mixed Boundary-Value Problem for the Hyperbolic Equation [in Russian], Moscow (1953).

  8. O. A. Ladyzhenskaya,Boundary-Value Problems of Mathematical Physics [in Russian], Moscow (1973).

  9. O. A. Ladyzhenskaya,Mathematical Theory of Viscous Incompressible Flow [in Russian], Moscow (1961).

  10. O. A. Ladyzhenskaya, “On integral estimates and on convergence of numerical methods for linear elliptic operators”,Vest. LGU,7, 60–69 (1958).

    Google Scholar 

  11. V. N. Judovich, “A two-dimensional problem on ideal incompressible flow”,Mat. Sb.,64, 562–588 (1964)

    Google Scholar 

  12. V. N. Sedenko, “Uniqueness theorem for the generalized solution of the initial-boundary-value problem arising from the nonlinear theory of oscillations of hollow shells with small longitudinal inertia”,Solid Mech.,6, 142–150 (1991).

    Google Scholar 

  13. O. A. Ladyzhenskaya, “On the non-stationary Navier-Stokes equations”,Vest. LGU, Ser. Mat., Mech. Astr., No. 19, 9–18 (1958).

    Google Scholar 

  14. O. A. Ladyzhenskaya, “Global solvability of the boundary-value problem for the Navier-Stokes equations in the case of two space variables”,Dokl. Akad. Nauk SSSR,123, 427–429 (1958).

    Google Scholar 

Download references

Authors
  1. O. A. Ladyzhenskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dewdicated to the memory of A. P. Oskolkov

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 243, 1997, pp. 138–152.

Translated by O. A. Ladyzhenskaya.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ladyzhenskaya, O.A. On the global unique solvability of some two-dimensional problems for the water solutions of polymers. J Math Sci 99, 888–897 (2000). https://doi.org/10.1007/BF02673597

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02673597

Keywords

Search

Navigation