Recent existence and regularity results for wave maps
Journées équations aux dérivées partielles (1997)
- page 1-7
- ISSN: 0752-0360
Access Full Article
topHow to cite
topStruwe, Michael. "Recent existence and regularity results for wave maps." Journées équations aux dérivées partielles (1997): 1-7. <http://eudml.org/doc/93341>.
@article{Struwe1997,
author = {Struwe, Michael},
journal = {Journées équations aux dérivées partielles},
keywords = {Cauchy problem; wave maps; regularity; existence},
language = {eng},
pages = {1-7},
publisher = {Ecole polytechnique},
title = {Recent existence and regularity results for wave maps},
url = {http://eudml.org/doc/93341},
year = {1997},
}
TY - JOUR
AU - Struwe, Michael
TI - Recent existence and regularity results for wave maps
JO - Journées équations aux dérivées partielles
PY - 1997
PB - Ecole polytechnique
SP - 1
EP - 7
LA - eng
KW - Cauchy problem; wave maps; regularity; existence
UR - http://eudml.org/doc/93341
ER -
References
top- [1] F. Bethuel : On the singular set of stationary harmonic maps, manusc. math. 78 (1993), 417-443. Zbl0792.53039MR94a:58047
- [2] Y. Choquet-Bruhat : Applications harmoniques hyperboliques, C.R. Acad. Sci. Paris Ser. I Math. 303 (1986), 109-113. Zbl0607.58011MR87h:58045
- [3] D. Christodoulon, A. Shadi Tahvildar-Zadeh : On the regularity of spherically symmetric wave maps, Comm. Pure Appl. Math. 46 (1993), 1041-1091. Zbl0744.58071MR94e:58030
- [4] R. Coifman, P.L. Lions, Y. Meyer, S. Semmes: Compensated compactness and Hardy spaces, J. Math. Pures Appl. 72 (1993), 247-286. Zbl0864.42009MR95d:46033
- [5] L.C. Evans : Partial regularity for stationary harmonic maps into spheres, Arch. Rat. Mech. Anal., 116 (1991), 101-113. Zbl0754.58007MR93m:58026
- [6] C. Fefferman, E.M. Stein: Hp spaces of several variables, Acta Math. 129 (1972), 137-193. Zbl0257.46078MR56 #6263
- [7] A. Freire : Global weak solutions of the wave map system to compact homogeneous spaces, preprint. Zbl0867.58019
- [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). Zbl0906.35061
- [9] A. Freire, S. Müller, M. Struwe : Weak compactness of wave maps and harmonic maps, Ann. Inst. H. Poincaré, Analyse Non-Linéaire (to appear). Zbl0924.58011
- [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. Zbl0512.58018MR84i:58027
- [11] C.-H. GuOn the Cauchy problem for harmonic maps defined on two-dimensional Minkowski space, Comm. Pure Appl. Math. 33 (1980), 727-737. Zbl0475.58005MR82g:58027
- [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. Zbl0728.35015MR92e:58055
- [13] S. Klainerman, M. Machedon : Space-time estimates for null forms and the local existence theorem, Comm. Pure Appl. Math. 46 (1993), 1221-1268. Zbl0803.35095MR94h:35137
- [14] S. Klainerman, M. Machedon : Smoothing estimates for null forms and applications, Duke Math. Journal 81 (1995) 99-133. Zbl0909.35094MR97h:35022
- [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. Zbl0704.49006MR87j:49012
- [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. Zbl0896.35086MR99b:58063
- [17] J. Shatah : Weak solutions and development of singularities in the SU(2) σ-model, Comm. Pure Appl. Math. 41 (1988) 459-469. Zbl0686.35081MR89f:58044
- [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. Zbl0830.35086MR95e:35132
- [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. Zbl0769.58015MR93c:58056
- [20] M. Struwe : Geometric Evolution Problems, preprint ETH Zürich (1992), in : IAS/Park City Math. Ser. 2 (1996), 259-339. Zbl0847.58012
- [21] Y. Zhou : preprint.
- [22] Y. Zhou : Global weak solutions for the 2+1 dimensional wave maps with small energy, preprint, 1995.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.