Skip to main content

Part of the book series: NATO Science Series ((NAII,volume 47))

Abstract

This paper provides an informal survey of the various mathematical structures that appear in the most basic models of fluid motion.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abraham, R., Marsden, J. & Ratiu, T. (1988) Manifolds, Tensor Analysis, and Applications. Springer Verlag.

    Google Scholar 

  2. Aris, R. (1962) Vectors, Tensors, and the Basic Equations of Fluid Mechanics. Dover Publications.

    Google Scholar 

  3. Arnol’d, V. (1989) Mathematical Methods in Classical Mechanics. Springer Verlag.

    Google Scholar 

  4. Arnol’d, V. & Khesin, B. (1998) Topological Methods in Hydrodynamics. Springer Verlag.

    Google Scholar 

  5. Batchelor, G.K. (1967) An Introduction to Fluid Mechanics. Cambridge University Press.

    Google Scholar 

  6. Boothby, W. (1986) An Introduction to Differentiable Manifolds and Riemannian Geometry. Academic Press.

    Google Scholar 

  7. Chorin, A. & Marsden, J. (1993) A Mathematical Introduction to Fluid Mechanics. Springer Verlag.

    Google Scholar 

  8. Christenson, C. & Voxman, W. (1998) Aspects of Topology. BCS Associates.

    Google Scholar 

  9. Flanders, H. (1963) Differential Forms with Applications to the Physical Sciences. Academic Press.

    Google Scholar 

  10. Ghrist, R. & Komendarczyk, R. (2001) Topological features of inviscid flows. In An Introduction to the Geometry and Topology of Fluid Flows (ed. R.L. Ricca), this volume. NATO-ASI Series: Mathematics, Kluwer, Dordrecht, The Netherlands.

    Google Scholar 

  11. Guillemin, V. & Pollack, A. (1974) Differential Topology. Prentice-Hall.

    Google Scholar 

  12. Halmos, P. (1950) Measure Theory. Van Nostrand.

    Google Scholar 

  13. Halmos, P. (1960) Naive Set Theory. Van Nostrand.

    Google Scholar 

  14. Hirsch, M. (1976) Differential Topology. Springer Verlag.

    Google Scholar 

  15. MacLane, S. (1998) Categories for the Working Mathematician. Springer Verlag.

    Google Scholar 

  16. Marsden, J. & Hughs, T. (1994) Mathematical Foundations of Elasticity. Dover Publications.

    Google Scholar 

  17. Milnor, J. (1965) Topology from the Differentiable Viewpoint. University Press of Virginia.

    Google Scholar 

  18. Milnor, J. (1969) Morse Theory. Princeton University Press.

    Google Scholar 

  19. Moser, J. (1965) On the volume elements on a manifold. Trans. Amer. Math. Soc. 120, 286–294.

    Article  MathSciNet  MATH  Google Scholar 

  20. Munkres, J. (1975) Topology. A First Course. Prentice-H all.

    Google Scholar 

  21. Oxtoby, J. & Ulam, S. (1941) Measure-preserving homeomorphisms and metrical transitivity. Ann. of Math. 42(2), 874–920.

    Article  MathSciNet  MATH  Google Scholar 

  22. Serrin, J. (1959) Mathematical Principles of Classical Fluid Mechanics. In Handbuch der Physik. Vol. VIII/1, Springer-Verlag.

    Google Scholar 

  23. Spivak, M. (1979) A Comprehensive Introduction to Differential Geometry. Vol. I-V. Publish or Perish, Inc..

    Google Scholar 

  24. Spivak, M. (1965) Calculus on Manifolds. W.A. Benjamin.

    Google Scholar 

  25. Tur, A. & Yanovsky, V. (1993) Invariants in dissipationless hydrodynamic media. J. Fluid Mech. 248, 67–106.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. Vilenkin, N. (1968) Stories about Sets. Academic Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Boyland, P. (2001). Fluid Mechanics and Mathematical Structures. In: Ricca, R.L. (eds) An Introduction to the Geometry and Topology of Fluid Flows. NATO Science Series, vol 47. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0446-6_6

Download citation

  • DOI: https://doi.org/10.1007/978-94-010-0446-6_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-0207-6

  • Online ISBN: 978-94-010-0446-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics