Potential Flow and Slightly Viscous Flow

  • A. J. Chorin
  • J. E. Marsden
Part of the Texts in Applied Mathematics book series (TAM, volume 4)


The goal of this chapter is to present a deeper study of the relationship between viscous and nonviscous flows. We begin with a more detailed study of inviscid irrotational flows, i.e., potential flows. Then we go on to study boundary layers, where the main difference between slightly viscous and inviscid flows originates.


Boundary Layer Euler Equation Viscous Flow Potential Flow Point Vortex 
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  1. C. Anderson and C. Greengard, SIAM J. SIal. Compo 22[1985], 413MathSciNetzbMATHGoogle Scholar
  2. R. Abraham and J. Marsden, Foundations of Mechanics, 2nd Edition [1978]zbMATHGoogle Scholar
  3. J.E. Marsden and A. Weinstein, Coadjoint orbits, vortices and Clebsch variables for incompressible fluids, Physica 7D [1983] 305–323,.MathSciNetCrossRefGoogle Scholar
  4. L. Onsager, Nuovo Cimento 6 (Suppl.) [1949]229MathSciNetCrossRefGoogle Scholar
  5. A.J. Chorin, J. Fluid Mech.57[1973]781MathSciNetCrossRefGoogle Scholar
  6. AJ. Chorin, SIAM J. Sci. Stat. Comp. 1[1980]1.MathSciNetzbMATHCrossRefGoogle Scholar
  7. O.H. Hald, SIAM J. Num. An. 16[1979]726MathSciNetzbMATHCrossRefGoogle Scholar
  8. T. Beale and A. Majda, Math. Comp. 39[1982]1–28,29–52MathSciNetzbMATHGoogle Scholar
  9. K. Gustaffson and J. Sethian, Vortex Flows, SIAM Publications, 1989.Google Scholar
  10. J. Heywood, Arch. Rat. Mech. 37[1970] 48–60, and Acta Math. 129[1972] 11–34MathSciNetzbMATHCrossRefGoogle Scholar
  11. O.A. Olejnik, Soviet Math. Dokl. [1968]Google Scholar
  12. J. Lamperti [1966] Probability, a Survey of the Mathematical Theory, Benjamin.Google Scholar
  13. G.K. Batchelor [1967] An Introduction to Fluid Mechanics, Cambridge Univ. PressGoogle Scholar
  14. J. Lighthill [1963] Introduction to Boundary Layer Theory, in Laminar Boundary Layers, edited by L. Rosenhead, Oxford Univ. Press.Google Scholar
  15. A.J. Chorin, J. Compo Phys.27[1978]428.zbMATHCrossRefGoogle Scholar
  16. A.J. Chorin, T.J.R. Hughes, M.J. McCracken and J.E. Marsden, Comm. Pure. Appl. Math. 31[1978]205MathSciNetzbMATHCrossRefGoogle Scholar
  17. C. Anderson, J. Compo Phys. 80[1989]72zbMATHCrossRefGoogle Scholar
  18. C. Marchioro and M. Pulvirenti, Vortex Methods in 2-dimensional Fluid Mechanics, Springer-Verlag, [1984]Google Scholar
  19. K. Gustaffson and J. Sethian, Vortex Flows, SIAM publications [1990].Google Scholar
  20. A. Chorin, J. Fluid Mech. 57[1973]785–796MathSciNetCrossRefGoogle Scholar
  21. J. Marsden, Bull. Am. Math. Soc. 80[1974]154–158MathSciNetzbMATHCrossRefGoogle Scholar
  22. G. Benfauo and M. Pulvirenti, Convergence of the Chorin-Marsdcn product fromula in the half plane, Comm. Math. Phys. 106[1986]427–458.MathSciNetCrossRefGoogle Scholar
  23. J. Marsden and M. McCracken [1976] The Hopf Bifurcation. Springer Applied Mathematics SerieszbMATHCrossRefGoogle Scholar
  24. D. Sallinger [1973] Lectures on Stability and Bifurcation Theory. Springer Lecture Notes 309.Google Scholar
  25. C.C. Lin [1955] The Theory of Hydrodynamic Stability, CambridgezbMATHGoogle Scholar
  26. S. Chandrasekar [1961] Hydrodynamic and Hydromagnetic Stability, Oxford.Google Scholar
  27. J. Marsden and T J.R. Hughes [1983] Mathematical Foundations of Elasticity, Prentice HallzbMATHGoogle Scholar
  28. M. Golubitsky. I. Stewart and D. Schaeffer [1988] Symmetry and Groups in Bifurcation Theory, Vol. II, Springer-Verlag for further infonnation and references.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • A. J. Chorin
    • 1
  • J. E. Marsden
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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