Harmonic maps of the hyperbolic space and development of singularities in wave maps and Yang-Mills fields

Thierry Cazenave; Jalal Shatah; A. Shadi Tahvildar-Zadeh

Annales de l'I.H.P. Physique théorique (1998)

  • Volume: 68, Issue: 3, page 315-349
  • ISSN: 0246-0211

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Cazenave, Thierry, Shatah, Jalal, and Tahvildar-Zadeh, A. Shadi. "Harmonic maps of the hyperbolic space and development of singularities in wave maps and Yang-Mills fields." Annales de l'I.H.P. Physique théorique 68.3 (1998): 315-349. <http://eudml.org/doc/76787>.

@article{Cazenave1998,
author = {Cazenave, Thierry, Shatah, Jalal, Tahvildar-Zadeh, A. Shadi},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {wave maps; Yang-Mills fields; harmonic maps},
language = {eng},
number = {3},
pages = {315-349},
publisher = {Gauthier-Villars},
title = {Harmonic maps of the hyperbolic space and development of singularities in wave maps and Yang-Mills fields},
url = {http://eudml.org/doc/76787},
volume = {68},
year = {1998},
}

TY - JOUR
AU - Cazenave, Thierry
AU - Shatah, Jalal
AU - Tahvildar-Zadeh, A. Shadi
TI - Harmonic maps of the hyperbolic space and development of singularities in wave maps and Yang-Mills fields
JO - Annales de l'I.H.P. Physique théorique
PY - 1998
PB - Gauthier-Villars
VL - 68
IS - 3
SP - 315
EP - 349
LA - eng
KW - wave maps; Yang-Mills fields; harmonic maps
UR - http://eudml.org/doc/76787
ER -

References

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  2. [2] M. Balabane, Ondes progressives et résultats d'explosion pour des systèmes non linéaires du premier ordre, C. R. Acad. Paris, série I, Vol. 302, 1986, pp. 211-214. Zbl0606.35013MR832046
  3. [3] P. Avilés, H.I. Choi and M.J. Micallef, Boundary behavior of harmonic maps on non-smooth domains and complete negatively curved manifolds, J. Func. Anal., Vol. 99, 1991, pp. 293-331. Zbl0805.53037MR1121616
  4. [4] O. Dumitrascu, Soluţii echivariante ale ecuaţiilor Yang-Mills, Stud. Cerc. Mat., 1982, Vol. 34(4), pp. 329-333. MR682374
  5. [5] J. Eells and A. Ratto, Harmonic Maps and Minimal Immersions, Princeton University Press, Princeton, NJ, 1993. Zbl0783.58003MR1242555
  6. [6] R.T. Glassey and W.A. Strauss, Some global solutions of the Yang-Mills equations in Minkowski space, Commun. Math. Phys., Vol. 81, 1981, pp. 171-187. Zbl0496.35055MR632755
  7. [7] M. Itoh, Invariant connections and Yang-Mills solutions, Trans. of the American Mathematical Society, Vol. 267(1), 1981, pp. 229-236. Zbl0473.53043MR621984
  8. [8] H. Karcher and J.C. Wood, Non-existence results and growth properties for harmonic maps and forms, J. Reine Angew. Math., Vol. 353, 1984, pp. 165-180. Zbl0544.58008MR765831
  9. [9] H. Lindblad, A sharp counterexample to the local existence of low-regularity solutions to nonlinear wave equations, Duke Math. J., Vol. 72, 1993, pp. 503-539. Zbl0797.35123MR1248683
  10. [10] H. Lindblad and C. Sogge, On existence and scattering with minimal regularity for semilinear wave equations, J. Func. Anal., Vol. 130, 1995, pp. 357-426. Zbl0846.35085MR1335386
  11. [11] G. Ponce and T. Sideris, Local regularity of nonlinear wave equations in three space dimensions, Comm. Partial Differential Equations, Vol. 18, 1993, pp. 169-177. Zbl0803.35096MR1211729
  12. [12] J. Shatah, Weak solutions and development of singularities in the SU(2) σ-model, Comm. Pure. Appl. Math., Vol. 41, 1988, pp. 459-469. Zbl0686.35081MR933231
  13. [13] J. Shatah and A. Tahvildar-Zadeh, On the Cauchy problem for equivariant wave maps, Comm. Pure Appl. Math, Vol. 47, 1993, pp. 719-754. Zbl0811.58059MR1278351
  14. [14] A. Tachikawa, Rotationally symmetric harmonic maps from a ball into a warped product manifold, Manus. Math., Vol. 53, 1985, pp. 235-254. Zbl0578.58008MR807098

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