Advertisement

Siberian Mathematical Journal

, Volume 31, Issue 2, pp 296–307 | Cite as

Asymptotic solution of the Navier-Stokes problem on the flow of a thin layer of fluid

  • S. A. Nazarov
Article

Keywords

Thin Layer Asymptotic Solution 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    O. Reynolds, Hydrodynamic Theory of Lubrication [Russian translation], Gostekhizdat, Moscow-Leningrad (1934).Google Scholar
  2. 2.
    N. P. Petrov, Hydrodynamic Theory of Lubrication: Selected Works [in Russian], Izd. Akad. Nauk SSSR, Moscow (1948).Google Scholar
  3. 3.
    G. Bayada and M. Chambat, “The transition between the Stokes equations and the Reynolds equation: a mathematical proof,” Appl. Math. Optim.,14, No. 1, 73–93 (1986).Google Scholar
  4. 4.
    A. L. Gol'denveiser, “Construction of an approximate theory of bending of a plate by the method of asymptotic integration of the equations of the theory of elasticity,” Prikl. Mat. Mekh.,26, No. 4, 668–686 (1962).Google Scholar
  5. 5.
    M. G. Dzhavadov, “Asymptotics of a solution of a boundary problem for second order elliptic equations in thin domains,” Differents. Uravn.,4, No. 10, 1901–1909 (1968).Google Scholar
  6. 6.
    E. I. Zino and E. A. Tropp, Asymptotic Methods in Problems of Thermal Conductivity and Thermelasticity [in Russian], LGU, Leningrad (1978).Google Scholar
  7. 7.
    S. A. Nazarov, “Structure of solutions of elliptic boundary problems in thin domains,” Vestn. LGU, No. 7, 65–68 (1982).Google Scholar
  8. 8.
    V. V. Kucherenko and V. A. Popov, “Asymptotics of solutions of problems of the theory of elasticity in thin domains,” Dokl. Akad. Nauk SSSR,274, No. 1 58–61 (1984).Google Scholar
  9. 9.
    V. L. Berdichevskii, Variational Principles of Mechanics of Continuous Media [in Russian], Nauk, Moscow (1983).Google Scholar
  10. 10.
    S. N. Leora, S. A. Nazarov, and A. V. Proskura, “Derivation of limit equations for elliptic problems in thin domains with the help of computers,” Zh. Vychisl. Mat. Mat. Fiz.,26, No. 7, 1032–1048 (1986).Google Scholar
  11. 11.
    S. Agmon and L. Nirenberg, “Properties of solutions of ordinary differential equations in Banach spaces,” Comm. Pure Appl. Math.,16, No. 1, 121–239 (1963).Google Scholar
  12. 12.
    V. A. Kondrat'ev, “Boundary problems for elliptic equations in domains with conical or corner points,” Tr. Mosk. Mat. Obshch.,16, 209–292 (1967).Google Scholar
  13. 13.
    V. G. Maz'ya and B. A. Plamenevskii, “Coefficients in asymptotic solutions of elliptic boundary problems in a domain with conical points,” Math. Nachr.,81, 25–82 (1978).Google Scholar
  14. 14.
    O. A. Ladyzhenskaya, Mathematical Questions of the Dynamics of a Viscous Fluid [in Russian], Nauka, Moscow (1970).Google Scholar
  15. 15.
    V. A. Solonnikov, “Solvability of a problem on the plane motion of a turbid viscous incompressible fluid partially filling a vessel,” Izd. Akad. Nauk SSR, Ser. Mat.,43, No. 1, 203–236 (1979).Google Scholar
  16. 16.
    R. Temam, Navier-Stokes Equation. Theory and Numerical Analysis [Russian translation], Mir, Moscow (1981).Google Scholar
  17. 17.
    V. G. Maz'ya and B. A. Plamenevskii, “Estimates in Lp and in Hölder classes and the Miranda-Agmon principle for solutions of elliptic boundary problems in domains with singular points on the boundary,” Math. Nachr.,76, 29–60 (1977).Google Scholar
  18. 18.
    S. Agmon, A. Douglis, and L. Nirenberg, “Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions,” Comm. Pure Appl. Math.,17, No. 1, 35–92 (1964).Google Scholar
  19. 19.
    V. A. Solonnikov, “Solvability of a three-dimensional problem with free boundary for a stationary system of Navier-Stokes equations,” Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst.,84, 252–285 (1979).Google Scholar
  20. 20.
    V. G. Maz'ya, B. A. Planmenevskii, and L. I. Stupyalis, “Three-dimensional problem of steady state motion of a fluid with free surface,” in: Differential Equations and their Application [in Russian], Vol. 23, Izdat. LitSSR, Vilnius (1979), pp. 29–153.Google Scholar
  21. 21.
    V. I. Malyi, “Asymptotic solution of the problem of compression of a layer of slightly compressible material,” in: Mechanics of Elastomers [in Russian], KPI, Krasnodar (1983), pp. 38–44.Google Scholar
  22. 22.
    L. V. Milyakova and K. F. Chernykh, “General linear theory of thinly-layered rubbermetallic elements,” Mekh. Tverd. Tela, No. 3, 110–120 (1986).Google Scholar
  23. 23.
    V. M. Mal'kov, “Linear theory of a thin layer of slightly compressible material,” Dokl. Akad. Nauk SSSR,293, No. 1, 42–44 (1987).Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • S. A. Nazarov

There are no affiliations available

Personalised recommendations