On global existence for nonlinear wave equations outside of convex obstacles

American Journal of Mathematics

Volumn 122, Issue 4, 2000, Pages 805-842

  Keel, Markus ^a   Smith, Hart F ^a   Sogge, Christopher D ^a  

^a NONE

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[No Author keywords available]

Indexed keywords

EID: 0006474474     PISSN: 00029327     EISSN: None     Source Type: Journal    
DOI: 10.1353/ajm.2000.0029     Document Type: Article

References (21)

1. D. Christodoulou, Solutions globales des equations de champ de Yang-Mills, C. R. Acad. Sci. Paris Ser. A, 293 (1981), 481-506.
2. _, Global solutions of nonlinear hyperbolic equations for small initial data, Comm. Pure Appl. Math. 39 (1986), 267-282.
3. V. Georgiev and P. P. Schirmer, Global existence of low regularity solutions of non-linear wave equations, Math. Z. 219 (1995), 1-19.
4. P. Godin, Global existence of solutions to some exterior radial quasilinear Cauchy-Dirichlet problems, Amer. J. Math. 117 (1995), 1475-1505.
5. N. Hayashi, Global existence of small radially symmetric solutions to quadratic nonlinear wave equations in an exterior domain, Manuscripta Math., 81 (1993), 15-39.
6. _, Global existence of small solutinos to quadratic nonlinear wave equatinos in an exterior domain, J. Funct. Anal. 131 (1995), 302-344.
7. L. Hörmander, Lectures on Nonlinear Hyperbolic Equations, Springer-Verlag, Berlin, 1977.
8. F. John, Nonlinear Wave Equations, Formation of Singularities, University Lecture Series, American Mathematical Society, Providence, RI, 1990.
9. S. Klainerman, Long Time Behavior of Solutions to Nonlinear Wave Equations, Proceedings of the International Congress of Mathematicians, Warsaw, 1982.
10. _, The null condition and global existence to nonlinear wave equations, Nonlinear Systems of Partial Differential Equations in Applied Mathematics, Part 1 (Santa Fe, NM, 1984), Lectures in Appl. Math., vol. 23, Amer. Math. Soc., Providence, RI, 1986, pp. 293-326.
11. S. Klainerman and M. Machedon, Space-time estimates for null forms and the local existence theorem, Comm. Pure Appl. Math. 46 (1993), 1221-1268.
12. P. D. Lax, C. S. Morawetz, and R. S. Phillips, Exponential decay of solutions of the wave equation in the exterior of a star-shaped obstacle, Comm. Pure Appl. Math. 16 (1963), 477-486.
13. P. D. Lax and S. Phillips, Scattering Theory, Revised Edition, Academic Press, San Diego, 1989.
14. G. Mockenhaupt, A. Seeger and C. Sogge, Local smoothing of Fourier integral operators and Carleson-Sjölin estimates, J. Amer. Math. Soc. 6 (1993), 65-130.
15. R. Penrose, Conformal treatment of infinity, Relativité, Groupes et Topologie, Gordon and Breach, New York, 1964, pp. 565-584.
16. Y. Shibata and Y. Tsutsumi, On a global existence theorem of small amplitude solutions for nonlinear wave equations in an exterior domain, Math. Z. 191 (1986), 165-169.
17. H. Smith and C. D. Sogge, On the critical semilinear wave equation outside convex obstacles, J. Amer. Math. Soc. 8 (1995), 879-916.
18. _, Global Strichartz estimates for nontrapping perturbations of the Laplacian, Comm. Partial Differential Equations (to appear).
19. _, Null form estimates for (1/2,1/2) symbols and local existence for a quasilinear Dirichletwave equation, Ann. Sci. École Norm. Sup. (to appear).
20. C. D. Sogge, On local existence for nonlinear wave equations satisfying variable coefficient null conditions, Comm. Partial Differential Equations 18 (1993), 1795-1821.
21. R. Strichartz, A priori estimates for the wave equation and some applications, J. Funct. Anal. 5 (1970), 218-235.