Advertisement

Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

Considerations regarding the mathematical basis for Prandtl's boundary layer theory

  • 105 Accesses

  • 24 Citations

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

Bibliography

  1. 1.

    Fife, P.C., Toward the validity of Prandtl's approximation in a boundary layer. Arch. Rational Mech. Anal. 18, 1–13 (1965).

  2. 2.

    Fife, P.C., The generation of a boundary layer in hydrodynamics. Arch. Rational Mech. Anal. 21, 286–302 (1966).

  3. 3.

    Krzyžanski, M., Certaines inégalités relatives aux solutions de l'équation parabolique lineare normale. Bull. Acad. Polonaise des Sciences. Ser. Math. Astr. Phys., 131–135 (1959).

  4. 4.

    Nickel, K., Die Prandtlschen Grenzschichtdifferentialgleichungen als Grenzfall der Navier-Stokesschen und der Eulerschen Differentialgleichungen. Arch. Rational Mech. Anal. 13, 1–14 (1963).

  5. 5.

    Miranda, C., Equazioni alle Derivate Parziali di Tipo Ellittico. Berlin-Göttingen-Heidelberg: Springer 1955.

  6. 6.

    Oleinik, O.A., On the system of equations of boundary layer theory [Russian]. Ž. Vyčisl.: Mat. i Mat. Fiz. 3, 489–507 (1963); — The Prandtl system of equations in boundary layer theory. Dokl. Akad. Nauk S.S.S.R. 150, Soviet Math. 4(3), 583–586 (1963).

  7. 7.

    Oleinik, O.A., & S.N. Kružkov, Quasilinear parabolic equations of second order with many variables [Russian]. Usp. Matem. Nauk 16, 116–155 (1961).

  8. 8.

    Serrin, J., Asymptotic behavior of velocity profiles in the Prandtl boundary layer theory. Proc. London Math. Soc. A299, 491–507 (1967).

  9. 9.

    Serrin, J., On the mathematical basis for Prandtl's boundary layer theory: an example. Following in this journal.

Download references

Author information

Additional information

This research was sponsored in part by the Air Force Office of Scientific Research., Office of Aerospace Research, under AFOSR Grant No. 883-67, and by the U.S. Fulbright Commission.

Communicated by J. Serrin

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Fife, P.C. Considerations regarding the mathematical basis for Prandtl's boundary layer theory. Arch. Rational Mech. Anal. 28, 184–216 (1968). https://doi.org/10.1007/BF00250926

Download citation

Keywords

  • Neural Network
  • Boundary Layer
  • Complex System
  • Nonlinear Dynamics
  • Electromagnetism