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On the existence of global vortex rings. (English) Zbl 0457.76020


MSC:

76B47 Vortex flows for incompressible inviscid fluids
35R05 PDEs with low regular coefficients and/or low regular data
35B99 Qualitative properties of solutions to partial differential equations

Citations:

Zbl 0282.76014
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Full Text: DOI

References:

[1] Agmon, S.; Douglis, A.; Nirenberg, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I-II, Comm. Pure Appl. Math., 12, 623-727 (1959) · Zbl 0093.10401 · doi:10.1002/cpa.3160120405
[2] Ambrosetti, A.; Rabinowitz, P., Dual variational methods in critical point theory and applications, J. Functional Analysis, 14, 349-381 (1973) · Zbl 0273.49063 · doi:10.1016/0022-1236(73)90051-7
[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. · Zbl 0345.35034
[4] Fraenkel, L. E.; Berger, M. S., A global theory of steady vortex rings in an ideal fluid, Acta Math., 132, 13-51 (1974) · Zbl 0282.76014 · doi:10.1007/BF02392107
[5] Gidas, B.; Ni, W.-M.; Nirenberg, L., Symmetry and related properties via maximum principle, Comm. Math. Phys., 68, 209-243 (1979) · Zbl 0425.35020 · doi:10.1007/BF01221125
[6] D. Gilbarg and N. S. Trudinger,Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1977. · Zbl 0361.35003
[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] Ni, W.-M., Some minimax principles and their applications in nonlinear elliptic equations, J. Analyse Math., 37, 248-275 (1980) · Zbl 0462.58016 · doi:10.1007/BF02797687
[9] M. H. Protter and H. F. Weinberger,Maximum Principles in Differential Equations, Prentice-Hall, 1967. · Zbl 0153.13602
[10] P. Rabinowitz,Variational methods and nonlinear eigenvalue problems, inEigenvalues in Nonlinear Problems, C.I.M.E., 1974, pp. 141-195.
[11] Vainberg, M. M., Variational Methods for the Study of Nonlinear Operators (1964), San Francisco: Holden-Day, San Francisco · Zbl 0122.35501
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