This is a preview of subscription content, log in via an institution to check access.
References
Agmon, S., The L p approach to the Dirichlet problem. Ann. Scuola Norm. Sup. Pisa (3) 13 (1959), 405–448.
Agmon, S., Douglis, A., & Nirenberg, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I. Comm. Pure Appl. Math. 12 (1959), 623–727.
Ambrosetti, A., & Mancini, G., On some free boundary problems. In Recent contributions to nonlinear partial differential equations (edited by H. Berestycki & H. Brézis). Pitman, 1981.
Amick, C. J., & Fraenkel, L. E., The uniqueness of Norbury's perturbation of Hill's spherical vortex. To appear.
Amick, C. J., & Fraenkel, L. E., Note on the equivalence of two variational principles for certain steady vortex rings. To appear.
Benjamin, T. B., The alliance of practical and analytical insights into the nonlinear problems of fluid mechanics. In Applications of methods of functional analysis to problems of mechanics, Lecture notes in math. 503. Springer, 1976.
Berestycki, H., Some free boundary problems in plasma physics and fluid mechanics. In Applications of nonlinear analysis in the physical sciences (edited by H. Amann, N. Bazley & K. Kirchgässner). Pitman, 1981.
Caffarelli, L. A., & Friedman, A., Asymptotic estimates for the plasma problem. Duke Math. J. 47 (1980), 705–742.
Chandrasekhar, S., Hydrodynamic and hydromagnetic stability. Oxford, 1961.
Ekeland, I., & Temam, R., Convex analysis and variational problems. North-Holland, 1976.
Esteban, M. J., Nonlinear elliptic problems in strip-like domains: symmetry of positive vortex rings. Nonlinear Analysis, Theory, Methods and Applications 7 (1983), 365–379.
Fraenkel, L. E., & Berger, M. S., A global theory of steady vortex rings in an ideal fluid. Acta Math. 132 (1974), 13–51.
Friedman, A., & Turkington, B., Vortex rings: existence and asymptotic estimates. Trans. Amer. Math. Soc. 268 (1981), 1–37.
Gidas, B., Ni, W.-M., & Nirenberg, L., Symmetry and related properties via the maximum principle. Comm. Math. Phys. 68 (1979), 209–243.
Gilbarg, D., & Trudinger, N. S., Elliptical partial differential equations of second order. Springer, 1977.
Giles, J. R., Convex analysis with application in differentiation of convex functions. Pitman, 1982.
Hill, M. J. M., On a spherical vortex. Philos. Trans. Roy. Soc. London A 185 (1894), 213–245.
Keady, G., & Kloeden, P. E., Maximum principles and an application to an elliptic boundary-value problem with a discontinuous nonlinearity. Research report, Dept. of Math., University of Western Australia, 1984.
Kinderlehrer, D., & Stampacchia, G., An introduction to variational inequalities and their applications. Academic Press, 1980.
Ni, W.-M., On the existence of global vortex rings. J. d'Analyse Math. 37 (1980), 208–247.
Nirenberg, L., On elliptic partial differential equations. Ann. Scuola Norm. Sup. Pisa (3) 13 (1959), 115–162.
Norbury, J., A steady vortex ring close to Hill's spherical vortex. Proc. Cambridge Philos. Soc. 72 (1972), 253–284.
Norbury, J., A family of steady vortex rings. J. Fluid Mech. 57 (1973), 417–431.
Serrin, J., A symmetry problem in potential theory. Arch. Rational Mech. Anal. 43 (1971), 304–318.
Author information
Authors and Affiliations
Additional information
Dedicated to James Serrin on the occasion of his 60 th birthday
Rights and permissions
About this article
Cite this article
Amick, C.J., Fraenkel, L.E. The uniqueness of Hill's spherical vortex. Arch. Rational Mech. Anal. 92, 91–119 (1986). https://doi.org/10.1007/BF00251252
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00251252