Almost global existence for solutions of semilinear Klein-Gordon equations with small weakly decaying Cauchy data

Communications in Partial Differential Equations

Volumn 25, Issue 11-12, 2000, Pages 2119-2169

  Delort, Jean Marc ^a   Fang, Daoyuan ^a,b  

^a UNIVERSITÉ PARIS 13   (France)

^b ZHEJIANG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037906740     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1080/03605300008821580     Document Type: Article

References (27)

1. J.-M. Bony: Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles nonlinéaires, Ann. Sci. École Norm. Sup. 14, (1981) 209-256.
2. J. Bourgain: Fourier transforms restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations, I, II, Geom. Funct. Anal. 3, (1993) 107-156, 202-262.
3. J. Bourgain: Appendix to [14].
4. J.-M. Delort: Sur le temps d'existence pour l'équation de Klein-Gardon semi-linéaire en dimension 1, Bull. Soc. Math. Fr. 125, (1997) 269-311.
5. J.-M. Delort: Temps d'existence pour l'équation de Klein-Gordon semi-linéaire à données petites périodiques, Amer. J. Math. 120, (1998) 663-689.
6. 2-estimates for wave equations, preprint, (1998).
7. V. Georgiev and P. Popivanov: Global solutions to the two-dimensional Klein-Gordon equations, Commun. Part. Diff. Eqs 16, (1991) 941-995.
8. L. Hörmander: The lifespan of classical solutions of non-linear hyperbolic equations, Springer Lectures Notes in Math. 1256, (1987) 214-280.
9. L. Hörmander: Lectures on Nonlinear Hyperbolic Differential Equations, Mathématiques et Applications 26, Springer, (1997).
10. M. Keel and T. Tao: Small data blow-up for semilinear Klein-Gordon equations, American Journal of Mathematics, 121, no 3, (1999), 629-669.
11. S. Klainerman: Global existence of small amplitude solutions to nonlinear Klein-Gordon equations in four space-time dimensions, Comm. Pure Appl. Math. 38, (1985) 631-641.
12. S. Klainerman and M. Machedon: Smoothing estimates for null forms and the local existence theorem, Comm. Pure Applied Math. 46, no 9 (1993) 1221-1268.
13. S. Klainerman and M. Machedon: Smoothing estimates for null forms and applications, Duke Math. J. 81, (1995-1996) 99-133.
14. S. Klainerman and M. Machedon: Remark on Strichartz Type Inequalities, IMRN no 5, (1996) 201-220.
15. s,δ, IMRN no 17, (1996) 853-865.
16. S. Klainerman and S. Selberg: Remark on the optimal regularity for equations of wave map type, Commun. Part. Diff. Eqs 22, no 5-6, (1997) 901-918.
17. 4+1. J. Amer. Math. Soc. 12 (1999), no. 1, 93-116.
18. R. Kosecki: The Unit Condition and Global Existence for a Class of Nonlinear Klein-Gordon Equations, Jour. Diff. Eq. 100, (1992) 257-268.
19. G. Lebeau: Personal communication.
20. H. Lindblad and C. Sogge: Restriction theorems and semilinear Klein-Gordon equations in (1 + 3)-dimensions, Duke Math. J. 85, (1996) 227-252.
21. K. Moriyama, S. Tonegawa and Y. Tsutsumi: Almost global existence of solutions for the quadratic semilinear Klein-Gordon equation in one space dimension, Funkcialaj Ekvacioj 40, no 2, (1997) 313-333.
22. T. Ozawa, K. Tsutaya and Y. Tsutsumi: Global existence and asymptotic behavior of solutions for the Klein-Gordon equations with quadratic nonlineanty in two space dimensions, Math. Z. 222, (1996) 341-362.
23. J. Shatah: Normal forms and quadratic nonlinear Klein-Gordon equations, Comm. Pure Appl. Math. 38, (1985) 685-696.
24. J. C. H. Simon and E. Taflin: The Cauchy problem for nonlinear Klein-Gordon equations, Commun. Math. Phys. 152, (1993) 433-478.
25. D. Tataru: Local and global results for wave maps I, Comm. Partial Differential Equations 23 (1998), no. 9-10, 1781-1793.
26. D. Tataru: On global existence and scattering for the wave maps equation, preprint, (1998).
27. B. Yordanov: Blow-up for the one-dimensional Klein-Gordon Equation with a cubic nonlinearity, preprint, (1996).