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On the mathematical theory of vortex sheets

  • Paul R. Garabedian
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1340)

Keywords

Rotor Blade Vortex Sheet Transonic Flow Vortex Filament Wing Section 
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.

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References

  1. [1]
    F. Bauer, O. Betancourt and P. Garabedian, Magnetohydrodynamic Equilibrium and Stability of Stellarators, Springer-Verlag, New York, 1984.CrossRefMATHGoogle Scholar
  2. [2]
    F. Bauer, P. Garabedian, A. Jameson and D. Korn, Supercritical Wing Sections II, a Handbook, Lecture Notes in Economics and Mathematical Systems 108, Springer-Verlag, New York, 1975.CrossRefMATHGoogle Scholar
  3. [3]
    G. Birkhoff, Helmholtz and Taylor instability, Amer. Math. Soc., Proc. Symp. Appl. Math. 12 (1962), 55–76.MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    R. Caflisch and O. Orellana, Long time existence for a slightly perturbed vortex sheet, to be published.Google Scholar
  5. [5]
    I.C. Chang, Transonic flow analysis for rotors, NASA TP-2375, 1984.Google Scholar
  6. [6]
    P. Garabedian, Partial Differential Equations, Chelsea, New York, 1986.MATHGoogle Scholar
  7. [7]
    P. Garabedian, H. Lewy and M. Schiffer, Axially symmetric cavitational flow, Ann. Math. 56 (1952), 560–602.MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    P. Garabedian and M. Schiffer, Convexity of domain functionals, J. Anal. Math. 2 (1953), 281–368.MathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    H. Grad, Toroidal containment of a plasma, Phys. Fluids 10 (1967), 137–154.CrossRefGoogle Scholar
  10. [10]
    A. Jameson, T. Baker and N. Weatherill, Calculation of inviscid transonic flow over a complete aircraft, AIAA Paper 86-0103, 1986.Google Scholar
  11. [11]
    D. Kinderlehrer and L. Nirenberg, Regularity in free boundary problems, Ann. Scuola Norm. Sup. Pisa, Ser. IV, 4 (1977), 373–391.MathSciNetMATHGoogle Scholar
  12. [12]
    R. Krasny, A study of singularity formation in a vortex sheet by the point vortex approximation, J. Fluid Mech. 186 (1986).Google Scholar
  13. [13]
    H. Lewy, Free surface flow in a gravity field, Comm. Pure Appl. Math. 5 (1952), 413–414.MathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    D. Moore, The spontaneous appearance of a singularity in the shape of an evolving vortex sheet, Proc. Roy. Soc. London A 365 (1979), 105–119.MathSciNetCrossRefMATHGoogle Scholar
  15. [15]
    D. Ross, Computation of the transonic flow about a swept wing in the presence of an engine nacelle, Research and Development Report DOE/ER/03077-267, Courant Inst. Math. Sci., N.Y.U., 1985.Google Scholar
  16. [16]
    L. Schwartz, A semi-analytic approach to the self-induced motion of vortex sheets, J. Fluid Mech. 111 (1981), 475–490.MathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    C. Sulem, P. Sulem, C. Bardos and U. Frisch, Finite time analyticity for the two and three dimensional Kelvin-Helmholtz instability, Comm. Math. Phys. 80 (1981), 485–516.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Paul R. Garabedian
    • 1
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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