Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2d corotational wave map system

Communications in Mathematical Physics

Volumn 284, Issue 1, 2008, Pages 203-225

  Côte, Raphaël ^a   Kenig, Carlos E ^b   Merle, Frank ^c  

^a CENTRE DE MATHÉMATIQUES LAURENT SCHWARTZ   (France)

^b UNIVERSITY OF CHICAGO   (United States)

^c UNIVERSITÉ DE CERGY PONTOISE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 53349165941     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-008-0604-4     Document Type: Article

References (13)

1. H. Bahouri P. Gérard 1999 High frequency approximation of solutions to critical nonlinear wave equations Amer. J. Math. 121 131 175
2. T. Cazenave J. Shatah A.S. Tahvildar-Zadeh 1998 Harmonic maps of the hyperbolic space and development of singularities in wave maps and Yang-Mills fields Ann. Inst. H. Poincaré Phys. Théor. 68 3 315 349
3. R. Côte 2005 Instability of harmonic maps for the (1+2)-dimensional equivariant Wave map system Int. Math. Res. Not. 57 3525 3549
4. P. Gérard 1998 Description du défaut de compacité de l'injection de Sobolev ESAIM Control Optim. Calc. Var. 3 213 233 (electronic)
5. Kenig, C.E., Merle, F.: Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear wave equation. To appear, Acta. Math
6. C.E. Kenig F. Merle 2006 Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrödinger equation in the radial case Invent. Math. 166 3 645 675
7. C.E. Kenig G. Ponce L. Vega 1993 Well-posedness and scattering result for the generalized Korteweg-De Vries equation via contraction principle Comm. Pure Appl. Math. 46 527 620
8. Krieger, J., Schlag, W., Tataru, D.: Renormalization and blow up for charge one equivariant critical wave maps. http://arXiv.org/list/math.AP/0610248 (2006)
9. Rodnianski, I., Sterbenz, J.: On the formation of singularities in the critical O(3) sigma-model. math.AP/0605023, 2006
10. Shatah, J., Struwe, M.: Geometric wave equations. Courant Lecture Notes in Mathematics, Vol. 2, New York: New York University / Courant Institute of Mathematical Sciences, 1998
11. J. Shatah A.S. Tahvildar-Zadeh 1994 On the Cauchy problem for equivariant wave maps Comm. Pure Appl. Math. 47 5 719 754
12. Stein, E.M.: Singular integrals and differentiability properties of functions. Princeton Mathematical Series, No. 30, Princeton, N.J: Princeton University Press, 1970
13. M. Struwe 2003 Equivariant wave maps in two space dimensions Comm. Pure Appl. Math. 56 7 815 823