Global weak solutions for 1 + 2 dimensional wave maps into homogeneous spaces

Yi Zhou

Annales de l'I.H.P. Analyse non linéaire (1999)

  • Volume: 16, Issue: 4, page 411-422
  • ISSN: 0294-1449

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Zhou, Yi. "Global weak solutions for $1+2$ dimensional wave maps into homogeneous spaces." Annales de l'I.H.P. Analyse non linéaire 16.4 (1999): 411-422. <http://eudml.org/doc/78470>.

@article{Zhou1999,
author = {Zhou, Yi},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Cauchy problem; wave maps},
language = {eng},
number = {4},
pages = {411-422},
publisher = {Gauthier-Villars},
title = {Global weak solutions for $1+2$ dimensional wave maps into homogeneous spaces},
url = {http://eudml.org/doc/78470},
volume = {16},
year = {1999},
}

TY - JOUR
AU - Zhou, Yi
TI - Global weak solutions for $1+2$ dimensional wave maps into homogeneous spaces
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1999
PB - Gauthier-Villars
VL - 16
IS - 4
SP - 411
EP - 422
LA - eng
KW - Cauchy problem; wave maps
UR - http://eudml.org/doc/78470
ER -

References

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  2. [2] A. Freire, Global weak solutions of the wave map system to compact homogeneous spaces, Preprint. Zbl0867.58019MR1421290
  3. [3] A. Freire, S. Müller, M. Struwe, Weak convergence of wave maps from (1+2)- dimensional Minkowski space to Riemannian manifold, Invent. Math. (to appear). Zbl0906.35061MR1483995
  4. [4] C.-H. Gu, On the Cauchy problem for harmonic maps defined on two-dimensional Minkowski space, Comm. Pure Appl. Math., Vol. 33, 1980, pp. 727-737. Zbl0475.58005MR596432
  5. [5] F. Hélein , Regularity of weakly harmonic map from a surface into a manifold with symmetries, Manuscripta Math., Vol. 70, 1991, pp. 203-218. Zbl0718.58019MR1085633
  6. [6] S. Klainerman and M. Machedon, Space-time estimates for null forms and the local existence theorem, Comm. Pure Appl. Math., Vol. 46, 1993, pp. 1221-1268. Zbl0803.35095MR1231427
  7. [7] S. Müller and M. Struwe, Global existence of wave maps in 1+2 dimensions with finite energy data, preprint. Zbl0896.35086MR1481698
  8. [8] F. Murat, Compacité par compensation, Ann. Scula. Norm. Pisa, Vol. 5, 1978, pp. 489-507. Zbl0399.46022MR506997
  9. [9] R. Schoen and K. Uhlenbeck, Boundary regularity and the Dirichlet problem for harmonic maps, J.Diff.Geom., Vol. 18, 1983, pp. 253-268. Zbl0547.58020MR710054
  10. [10] J. Shatah, Weak solutions and development of singularity in the SU(2) σ-model, Comm. Pure Appl. Math., Vol. 41, 1988, pp. 459-469. Zbl0686.35081MR933231
  11. [11] L. Tartar, Compensated compactness and applications to p.d.e. Nonlinear Analysis and Mechanics, Heriot-Watt symposium, R. J. KNOPS, Vol. 4, 1979, pp. 136-212. Zbl0437.35004MR584398
  12. [12] Y. Zhou, Local existence with minimal regularity for nonlinear wave equations, Amer. J. Math. (to appear). Zbl0881.35077MR1448218
  13. [13] Y. Zhou, Remarks on local regularity for two space dimensional wave maps, J.Partial Differential Equations (to appear). Zbl0891.35103MR1443568
  14. [14] Y. Zhou, Uniqueness of weak solution of 1+1 dimensional wave maps, Math. Z. (to appear). Zbl0940.35141
  15. [15] Y. Zhou, An Lp theorem for the compensated compactness, Proceedings of royal society of Edinburgh, Vol. 122 A, 1992, pp. 177-189. Zbl0815.46031MR1190238

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