Global weak solutions for $1+2$ dimensional wave maps into homogeneous spaces
Annales de l'I.H.P. Analyse non linéaire, Volume 16 (1999) no. 4, p. 411-422
@article{AIHPC_1999__16_4_411_0,
author = {Zhou, Yi},
title = {Global weak solutions for $1+2$ dimensional wave maps into homogeneous spaces},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Gauthier-Villars},
volume = {16},
number = {4},
year = {1999},
pages = {411-422},
zbl = {0997.58012},
mrnumber = {1697560},
language = {en},
url = {http://www.numdam.org/item/AIHPC_1999__16_4_411_0}
}

Zhou, Yi. Global weak solutions for $1+2$ dimensional wave maps into homogeneous spaces. Annales de l'I.H.P. Analyse non linéaire, Volume 16 (1999) no. 4, pp. 411-422. http://www.numdam.org/item/AIHPC_1999__16_4_411_0/

[1] D. Christodoulou and A.S. Tahvildar-Zadeh, On the regularity of spherically symmetric wave maps, Comm. Pure Appl. Math., Vol. 46, 1993, pp. 1041-1091. | MR 1223662 | Zbl 0744.58071

[2] A. Freire, Global weak solutions of the wave map system to compact homogeneous spaces, Preprint. | MR 1421290

[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). | MR 1483995 | Zbl 0906.35061

[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. | MR 596432 | Zbl 0475.58005

[5] F. Hélein , Regularity of weakly harmonic map from a surface into a manifold with symmetries, Manuscripta Math., Vol. 70, 1991, pp. 203-218. | MR 1085633 | Zbl 0718.58019

[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. | MR 1231427 | Zbl 0803.35095

[7] S. Müller and M. Struwe, Global existence of wave maps in 1+2 dimensions with finite energy data, preprint. | MR 1481698

[8] F. Murat, Compacité par compensation, Ann. Scula. Norm. Pisa, Vol. 5, 1978, pp. 489-507. | Numdam | MR 506997 | Zbl 0399.46022

[9] R. Schoen and K. Uhlenbeck, Boundary regularity and the Dirichlet problem for harmonic maps, J.Diff.Geom., Vol. 18, 1983, pp. 253-268. | MR 710054 | Zbl 0547.58020

[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. | MR 933231 | Zbl 0686.35081

[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. | MR 584398 | Zbl 0437.35004

[12] Y. Zhou, Local existence with minimal regularity for nonlinear wave equations, Amer. J. Math. (to appear). | MR 1448218 | Zbl 0881.35077

[13] Y. Zhou, Remarks on local regularity for two space dimensional wave maps, J.Partial Differential Equations (to appear). | MR 1443568 | Zbl 0891.35103

[14] Y. Zhou, Uniqueness of weak solution of 1+1 dimensional wave maps, Math. Z. (to appear). | Zbl 0940.35141

[15] Y. Zhou, An Lp theorem for the compensated compactness, Proceedings of royal society of Edinburgh, Vol. 122 A, 1992, pp. 177-189. | MR 1190238 | Zbl 0815.46031