Skip to main content
SpringerLink
Log in
Book cover

Variational and Free Boundary Problems pp 111–134Cite as

Axisymmetric MHD Equilibria from Kruskal-Kulsrud to Grad

  • Conference paper

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 53))

Abstract

We provide a rigorous proof of the equivalence of the Kruskal-Kulsrud and Grad variational problems and show that minimizers are weak solutions of the associated Euler-Lagrange equations.

Partially supported under NSF grant # DMS 8904935.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   139.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Beltrami, E., Sui principii fondamentali dell’ idrodinamica razionali, Mem. della Accademia della Scienze dell’ Istituto di Bologna, Serie 3 no. 1 (1871), pp. 431–476.

    Google Scholar 

  2. Courant, R., Hilbert, D., Methods of Mathematical Physics, II, Interscience, New York (1962).

    MATH  Google Scholar 

  3. Crandall, M., Tartar, LUC, Some relations between non expansive and order preserving mappings, Proc. Amer. Math. Soc., 78 (1980), pp. 385–390.

    Article  MathSciNet  MATH  Google Scholar 

  4. Eydeland, A., Spruck, J., Turkington, B., Multi constrained variational problems of nonlinear eigenvalue type: new formulations and algorithms, Math. of Computation, 55 no. 192 (1990), pp. 509–535.

    Article  MathSciNet  MATH  Google Scholar 

  5. Eydeland, A., Spruce, J., Turkington, B., A computational method for multi constrained variational problems in magnetohydrodynamics, to appear.

    Google Scholar 

  6. Federer, H., Geometric Measure Theory, Springer Verlag, Berlin-Heidelberg-New York, 1969.

    MATH  Google Scholar 

  7. Garabedian, P., Partial Differential Equations, 2nd ed., Chelsea, New York, 1986.

    Google Scholar 

  8. Grad, H., Hu, P.N., AND Stevens, D.C., Adiabatic evolution of plasma equilibria, Proc. Nat. Acad. Sci. U.S.A., 72 (1975), pp. 3789–3793.

    Article  Google Scholar 

  9. Kruskal, M., Kulsrud, R., Plasma equilibria in a toroid, Physics of Fluids, 4 (1958), pp. 265–274.

    Article  MathSciNet  Google Scholar 

  10. Laurence, P., Stredulinsky, E., A new approach to queer differential equations, Comm. Pure Appl. Math., 38 (1985), pp. 333–335.

    Article  MathSciNet  MATH  Google Scholar 

  11. Mossino, J., Rakotoson, J., Isoperimetric inequalities in parabolic equations, Ann. Scuola Norm. Sup. Pisa, (IV)/3 (1986), pp. 51–73.

    MathSciNet  Google Scholar 

  12. Mossino, J., Temam, R., Directional derivative of the rearrangement mapping and applications to a queer differential equation in plasma physics, Duke Math. J., 41 (1981), pp. 475–495.

    Article  MathSciNet  Google Scholar 

  13. Roberts, P., An Introduction to Magnetohydrodynamics, American Elsevier, New York, 1967.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Rome, Rome, Italy

    Peter Lawrence

  2. Richland Center, University of Wisconsin-Richland, Wisconsin, 53581, USA

    Edward Stredulinsky

Authors
  1. Peter Lawrence
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Edward Stredulinsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute for Mathematics and its Applications, University of Minnesota, 55455, Minneapolis, MN, USA

    Avner Friedman

  2. Department of Mathematics, Johns Hopkins University, 21218, Baltimore, MD, USA

    Joel Spruck

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag New York, Inc.

About this paper

Cite this paper

Lawrence, P., Stredulinsky, E. (1993). Axisymmetric MHD Equilibria from Kruskal-Kulsrud to Grad. In: Friedman, A., Spruck, J. (eds) Variational and Free Boundary Problems. The IMA Volumes in Mathematics and its Applications, vol 53. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8357-4_8

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-8357-4_8

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8359-8

  • Online ISBN: 978-1-4613-8357-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation