Skip to main content
Log in

On the existence of global vortex rings

  • Published:
Journal d’Analyse Mathématique Aims and scope

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. S. Agmon, A. Douglis and L. Nirenberg,Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I–II, Comm. Pure Appl. Math.12 (1959), 623–727;17 (1964), 35–92.

    Article  MATH  MathSciNet  Google Scholar 

  2. A. Ambrosetti and P. Rabinowitz,Dual variational methods in critical point theory and applications, J. Functional Analysis14 (1973), 349–381.

    Article  MATH  MathSciNet  Google Scholar 

  3. M. S. Berger and L. E. Fraenkel,Global free boundary problems and the calculus of variations in the large, Lecture Notes in Mathematics503, Springer-Verlag, pp. 186–192.

  4. L. E. Fraenkel and M. S. Berger,A global theory of steady vortex rings in an ideal fluid, Acta Math.132 (1974), 13–51.

    Article  MATH  MathSciNet  Google Scholar 

  5. B. Gidas, W.-M. Ni and L. Nirenberg,Symmetry and related properties via maximum principle, Comm. Math. Phys.68 (1979), 209–243.

    Article  MATH  MathSciNet  Google Scholar 

  6. D. Gilbarg and N. S. Trudinger,Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1977.

  7. W.-M. Ni,Some minimax principles with applications in nonlinear elliptic boundary value problems and global vortex flow, Ph.D. Thesis, New York University, June 1979.

  8. W.-M. Ni,Some minimax principles and their applications in nonlinear elliptic equations, J. Analyse Math.37 (1980), 248–275.

    Article  MATH  MathSciNet  Google Scholar 

  9. M. H. Protter and H. F. Weinberger,Maximum Principles in Differential Equations, Prentice-Hall, 1967.

  10. P. Rabinowitz,Variational methods and nonlinear eigenvalue problems, inEigenvalues in Nonlinear Problems, C.I.M.E., 1974, pp. 141–195.

  11. M. M. Vainberg,Variational Methods for the Study of Nonlinear Operators, Holden-Day, San Francisco, 1964

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Supported in part by a grant from the National Science Foundation.

The results of this paper were obtained while the author was partially supported by U. S. Army Research Office grant No. DAA-29-78-6-0127 at Courant Institute, New York University.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ni, WM. On the existence of global vortex rings. J. Anal. Math. 37, 208–247 (1980). https://doi.org/10.1007/BF02797686

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02797686

Navigation