Global regularity for a logarithmically supercritical defocusing nonlinear wave equation for spherically symmetric data

Journal of Hyperbolic Differential Equations

Volumn 4, Issue 2, 2007, Pages 259-265

  Tao, Terence ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Endpoint Strichartz estimate; Morawetz inequality; Radical Sobolev inequality

Indexed keywords

EID: 34249855088     PISSN: 02198916     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219891607001124     Document Type: Article

References (15)

1. J. T. Beale, T. Kato and A. Majda, Remarks on the breakdown of smooth solutions for the 3-D Euler equations, Commun. Math. Phys. 94 (1984) 61-66.
2. M. Christ, J. Colliander and T. Tao, Ill-posedness for nonlinear Schrodinger and wave equations, to appear in Ann. Inst Henri Poincaré.
3. J. Ginibre, A. Soffer and G. Velo, The global Cauchy problem for the critical nonlinear wave equation, J. Funct. Anal. 110 (1992) 96-130.
4. J. Ginibre and G. Velo, Generalized Strichartz inequalities for the wave equation, J. Funct. Anal. 133 (1995) 50-68.
5. M. Grillakis, Regularity and asymptotic behaviour of the wave equation with a critical nonlinearity, Ann. Math. 132 (1990) 485-509.
6. M. Grillakis, Regularity for the wave equation with a critical nonlinearity, Commun. Pure Appl. Math. 45 (1992) 749-774.
7. L. Kapitanski, Global and unique weak solutions of nonlinear wave equations, Math. Res. Lett. 1 (1994) 211-223.
8. M. Keel and T. Tao, Endpoint Strichartz estimates, Amer. J. Math. 120 (1998) 955-980.
9. S. Klainerman and M. Machedon, Space-time estimates for null forms and the local existence theorem, Commun. Pure Appl. Math. 46 (1993) 1221-1268.
10. G. Lebeau, Nonlinear optics and supercritical wave equation, Hommage Pascal Laubin. Bull. Soc. Roy. Liége 70(4-6) (2001, 2002) 267-306.
11. G. Lebeau, Perte de régularité pour les équations d'ondes sur-critiques, Bull. Soc. Math. France 133(1) (2005) 145-157.
12. J. Shatah and M. Struwe, Geometric Wave Equations, Courant Lecture Notes in Mathematics, Vol. 2 (1998).
13. C. D. Sogge, Lectures on Nonlinear Wave Equations, Monographs in Analysis II (International Press, 1995).
14. 5 Klein-Gordon equation, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 15 (1988) 495-513.
15. T. Tao, Spacetime bounds for the energy-critical nonlinear wave equation in three spatial dimensions, preprint.