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Volumn 11, Issue 1, 2003, Pages 49-83

On the well-posedness of the wave map problem in high dimensions

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EID: 4043171934     PISSN: 10198385     EISSN: None     Source Type: Journal    
DOI: 10.4310/CAG.2003.v11.n1.a4     Document Type: Article
Times cited : (57)

References (26)
  • 1
    • 0002358697 scopus 로고
    • Approximations in trace spaces defined between mainifolds
    • F. Bethuel, Approximations in trace spaces defined between mainifolds, Nonlinear Analysis, 24, no. 1 (1995), 121-130.
    • (1995) Nonlinear Analysis , vol.24 , Issue.1 , pp. 121-130
    • Bethuel, F.1
  • 2
    • 0001363761 scopus 로고
    • The approximation problem for Sobolev maps between two manifolds
    • F. Bethuel, The approximation problem for Sobolev maps between two manifolds, Acta Math. 167, no. 3-4 (1991), 153-206.
    • (1991) Acta Math. , vol.167 , Issue.3-4 , pp. 153-206
    • Bethuel, F.1
  • 3
    • 84990569166 scopus 로고
    • On the regularity of spherically symmetric wave map
    • D. Christodoulou and S. Tahvildar-Zadeh, On the regularity of spherically symmetric wave map, Comm. Pure Appl. Math 46 (1993), 1041-1091.
    • (1993) Comm. Pure Appl. Math , vol.46 , pp. 1041-1091
    • Christodoulou, D.1    Tahvildar-Zadeh, S.2
  • 5
    • 0007043133 scopus 로고    scopus 로고
    • Classical solutions for the equivariant wave map in 1+2 dimensions
    • to appear
    • M. Grillakis, Classical solutions for the equivariant wave map in 1+2 dimensions, Indiana Univ. Math. J., to appear.
    • Indiana Univ. Math. J.
    • Grillakis, M.1
  • 6
    • 0001138601 scopus 로고    scopus 로고
    • Endpoint strichartz estimates
    • M. Keel and T. Tao, Endpoint Strichartz estimates Amer. Math. J., 120 (1998), 955-980.
    • (1998) Amer. Math. J. , vol.120 , pp. 955-980
    • Keel, M.1    Tao, T.2
  • 7
    • 0001646511 scopus 로고    scopus 로고
    • 1+1 for rough data
    • 1+1 for rough data, IMRN, 21 (1998), 1117-1156.
    • (1998) IMRN , vol.21 , pp. 1117-1156
    • Keel, M.1    Tao, T.2
  • 8
    • 84990576528 scopus 로고
    • Space-time estimates for null forms and the local existence
    • S. Klainerman and M. Machedon, Space-time estimates for null forms and the local existence, Comm. Pure Appl. Math., 46 no. 9 (1993), 1221-1268.
    • (1993) Comm. Pure Appl. Math. , vol.46 , Issue.9 , pp. 1221-1268
    • Klainerman, S.1    Machedon, M.2
  • 9
    • 84973999554 scopus 로고
    • Smoothing estimates for null forms and applications
    • S. Klainerman and M. Machedon, Smoothing estimates for null forms and applications, Duke Math J., 81 (1995), 99-133.
    • (1995) Duke Math J. , vol.81 , pp. 99-133
    • Klainerman, S.1    Machedon, M.2
  • 10
    • 0001253203 scopus 로고    scopus 로고
    • On the optimal local regularity for gauge fields theories
    • S. Klainerman and M. Machedon, On the optimal local regularity for gauge fields theories, Diff. and Integral Eqs., 10 (1997), 1019-1030.
    • (1997) Diff. and Integral Eqs. , vol.10 , pp. 1019-1030
    • Klainerman, S.1    Machedon, M.2
  • 11
    • 0010287924 scopus 로고    scopus 로고
    • On the global regularity of wave maps in the critical Sobolev norm
    • S. Klainerman and I. Rodnianski, On the global regularity of wave maps in the critical Sobolev norm, IMRN, 13 (2001), 655-677.
    • (2001) IMRN , vol.13 , pp. 655-677
    • Klainerman, S.1    Rodnianski, I.2
  • 12
    • 0001185364 scopus 로고    scopus 로고
    • Remarks on the optimal regularity for equations of wave maps type
    • S. Klainerman and S. Selberg, Remarks on the optimal regularity for equations of wave maps type, Comm. PDE, 22 (1997), 901-918.
    • (1997) Comm. PDE , vol.22 , pp. 901-918
    • Klainerman, S.1    Selberg, S.2
  • 17
    • 84990635786 scopus 로고
    • On the Cauchy problem for equivariant wave maps
    • J. Shatah and S. Tahvildar-Zadeh, On the Cauchy problem for equivariant wave maps, Comm. Pure Appl. Math., 47 (1994), 719-753.
    • (1994) Comm. Pure Appl. Math. , vol.47 , pp. 719-753
    • Shatah, J.1    Tahvildar-Zadeh, S.2
  • 18
    • 0031115723 scopus 로고    scopus 로고
    • On the stability of stationary wave maps
    • J. Shatah and S. Tahvildar-Zadeh, On the stability of stationary wave maps, Comm. Math. Phys., 185, no. 1 (1997), 231-256.
    • (1997) Comm. Math. Phys. , vol.185 , Issue.1 , pp. 231-256
    • Shatah, J.1    Tahvildar-Zadeh, S.2
  • 20
    • 2442546581 scopus 로고
    • Regularity results for harmonic maps of Minkowski space
    • Nematics, Coron et al., eds
    • M. Struwe, Regularity results for harmonic maps of Minkowski space, Nematics, Coron et al., eds. NATO ASI SER. C 332 (1991), 357-369.
    • (1991) NATO ASI SER. C , vol.332 , pp. 357-369
    • Struwe, M.1
  • 21
    • 0002341651 scopus 로고    scopus 로고
    • Geometric evolution problems
    • M. Struwe, Geometric Evolution Problems, IAS/Park City Math. Series 2 (1996), 259-339.
    • (1996) IAS/Park City Math. Series , vol.2 , pp. 259-339
    • Struwe, M.1
  • 22
    • 18844483049 scopus 로고    scopus 로고
    • Global regularity of wave maps I. Small critical Sobolev norm in high dimension
    • T. Tao, Global regularity of wave maps I. Small critical Sobolev norm in high dimension, IMRN 7 (2001), 299-328.
    • (2001) IMRN , vol.7 , pp. 299-328
    • Tao, T.1
  • 23
    • 85039498490 scopus 로고    scopus 로고
    • Global regularity of wave maps II. Small energy in two dimensions
    • to appear
    • T. Tao, Global regularity of wave maps II. Small energy in two dimensions, Comm. Math. Phys. to appear.
    • Comm. Math. Phys.
    • Tao, T.1
  • 24
    • 0000312262 scopus 로고    scopus 로고
    • Local and global results for wave maps I
    • D. Tataru, Local and global results for wave maps I, Comm. in PDE 23 (1998), 1781-1793.
    • (1998) Comm. in PDE , vol.23 , pp. 1781-1793
    • Tataru, D.1
  • 25
    • 85039502308 scopus 로고    scopus 로고
    • On global existence and scattering for the wave maps equation
    • to appear
    • D. Tataru, On global existence and scattering for the wave maps equation, Amer. J. Math (to appear).
    • Amer. J. Math
    • Tataru, D.1


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