Recent existence and regularity results for wave maps
Journées équations aux dérivées partielles (1997), article no. 17, 7 p. 
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     author = {Struwe, Michael},
     title = {Recent existence and regularity results for wave maps},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {17},
     pages = {1--7},
     publisher = {Ecole polytechnique},
     year = {1997},
     zbl = {01808675},
     language = {en},
     url = {http://archive.numdam.org/item/JEDP_1997____A17_0/}
}
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Struwe, Michael. Recent existence and regularity results for wave maps. Journées équations aux dérivées partielles (1997), article  no. 17, 7 p. http://archive.numdam.org/item/JEDP_1997____A17_0/

[1] F. Bethuel : On the singular set of stationary harmonic maps, manusc. math. 78 (1993), 417-443. | MR | Zbl

[2] Y. Choquet-Bruhat : Applications harmoniques hyperboliques, C.R. Acad. Sci. Paris Ser. I Math. 303 (1986), 109-113. | MR | Zbl

[3] D. Christodoulon, A. Shadi Tahvildar-Zadeh : On the regularity of spherically symmetric wave maps, Comm. Pure Appl. Math. 46 (1993), 1041-1091. | MR | Zbl

[4] R. Coifman, P.L. Lions, Y. Meyer, S. Semmes: Compensated compactness and Hardy spaces, J. Math. Pures Appl. 72 (1993), 247-286. | MR | Zbl

[5] L.C. Evans : Partial regularity for stationary harmonic maps into spheres, Arch. Rat. Mech. Anal., 116 (1991), 101-113. | MR | Zbl

[6] C. Fefferman, E.M. Stein: Hp spaces of several variables, Acta Math. 129 (1972), 137-193. | MR | Zbl

[7] A. Freire : Global weak solutions of the wave map system to compact homogeneous spaces, preprint. | Zbl

[8] A. Freire, S. Müller, M. Struwe: Weak convergence of harmonic maps from (2+1)-dimensional Minkowski space to Riemannian manifolds, Invent. math. (to appear). | Zbl

[9] A. Freire, S. Müller, M. Struwe : Weak compactness of wave maps and harmonic maps, Ann. Inst. H. Poincaré, Analyse Non-Linéaire (to appear). | Numdam | Zbl

[10] J. Ginibre, G. Velo : The Cauchy problem for the O(N), ℂP(N - 1) and Gℂ(N, P) models, Ann. Physics 142 (1982), 393-415. | MR | Zbl

[11] C.-H. Gu On the Cauchy problem for harmonic maps defined on two-dimensional Minkowski space, Comm. Pure Appl. Math. 33 (1980), 727-737. | MR | Zbl

[12] F. Hélein : Regularité des applications faiblement harmoniques entre une surface et une varitée Riemannienne, C.R. Acad. Sci. Paris Ser. I Math. 312 (1991) 591-596. | MR | Zbl

[13] S. Klainerman, M. Machedon : Space-time estimates for null forms and the local existence theorem, Comm. Pure Appl. Math. 46 (1993), 1221-1268. | MR | Zbl

[14] S. Klainerman, M. Machedon : Smoothing estimates for null forms and applications, Duke Math. Journal 81 (1995) 99-133. | MR | Zbl

[15] P.L. Lions : The concentration compactness principle in the calculs of variations, the limit case, Part 2, Rev. Mat. Iberoam. 1/2 (1985), 45-121. | MR | Zbl

[16] S. Müller, M. Struwe : Global existence of wave maps in 1 + 2 dimensions with finite energy data, Topological methods in nonlinear analysis 7 (1996), 245-259. | MR | Zbl

[17] J. Shatah : Weak solutions and development of singularities in the SU(2) σ-model, Comm. Pure Appl. Math. 41 (1988) 459-469. | MR | Zbl

[18] J. Shatah, M. Struwe : Well-posedness in the energy space for semilinear wave equations with critical growth, Inter. Math. Res. Notices 7 (1994), 303-309. | MR | Zbl

[19] J. Shatah, A. Tahvildar-Zadeh : Regularity of harmonic maps from the Minkowski space into rotationally symmetric manifolds, Comm. Pure Appl. Math. 45 (1992), 947-971. | MR | Zbl

[20] M. Struwe : Geometric Evolution Problems, preprint ETH Zürich (1992), in : IAS/Park City Math. Ser. 2 (1996), 259-339. | Zbl

[21] Y. Zhou : preprint.

[22] Y. Zhou : Global weak solutions for the 2+1 dimensional wave maps with small energy, preprint, 1995.