Weighted Strichartz estimates and global existence for semilinear wave equations

American Journal of Mathematics

Volumn 119, Issue 6, 1997, Pages 1291-1319

  Georgiev, Vladimir ^a   Lindblad, Hans ^a   Sogge, Christopher D ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001726448     PISSN: 00029327     EISSN: None     Source Type: Journal    
DOI: 10.1353/ajm.1997.0038     Document Type: Article

References (26)

1. J. Bourgain, Averages in the plane over convex curves and maximal operators, J. Anal. Math. 47 (1986), 69-85.
2. V. Georgiev, Weighted estimate for the wave equation, Nonlinear Waves. Proceedings of the Fourth MSJ International Research Institute, vol. 1, Hokkaido Univ., 1996, pp. 71-80.
3. R. Glassey. Existence in the large for □u = F(u) in two dimensions, Math. Z. 178 (1981), 233-261.
4. L. Hörmander, Fourier integrals I, Acta Math. 127 (1971), 79-183.
5. _, The Analysis of Linear Partial Differential Operators I-IV, Springer-Verlag, New York, 1985.
6. F. John, Blow-up of solutions of nonlinear wave equations in three space dimensions, Manuscripta Math. 28 (1979), 235-265.
7. H. Kubo, On the critical decay and power for semilinear wave equations in odd space dimensions, preprint.
8. H. Lindblad and C. D. Sogge, On existence and scattering with minimal regularity for semilinear wave equations, J. Funct. Anal. 130 (1995), 357-126.
9. _, Long-time existence for small amplitude semilinear wave equations, Amer. J. Math. 118 (1996), 1047-1135.
10. _, Restriction theorems and semilinear wave equations in (1 + 3)-dimensions, Duke Math. J. (to appear).
11. M. A. Rammaha, Finite-time blow-up for nonlinear wave equations in high dimensions, Comm. Partial Differential Equations 12 (1987), 677-700.
12. p for the critical value of p, Proc. Royal Soc. Edinburgh Sect. A 101 (1985), 31-44.
13. A. Seeger, C. D. Sogge, and E. M. Stein, Regularity properties of Fourier integrals, Ann. of Math. 134 (1991), 231-251.
14. I. Segal, Space-time decay for solutions of wave equations, Adv. Math. 22 (1976), 305-311.
15. T. Sideris, Nonexistent of global solutions to semilinear wave equations in high dimensions, Comm. Partial Differential Equations 12 (1987), 378-406.
16. C. D. Sogge, Propagation of singularities and maximal functions in the plane, Invent. Math. 104 (1991), 349-376.
17. _, Fourier Integrals in Classical Analysis, Cambridge Univ. Press, Cambridge, 1993.
18. _, Lectures on Nonlinear Wave Equations, International Press, Cambridge, MA. 1995.
19. C. D. Sogge and E. M. Stein, Averages of functions over hypersurfaces: Smoothness of generalized Radon transforms, J. Anal. Math. 54 (1990), 165-188.
20. E. M. Stein, Interpolation of linear operators, Trans. Amer. Math. Soc. 83 (1956), 482-492.
21. W. Strauss, Nonlinear scattering theory, Scattering Theory in Mathematical Physics, Reidel, Dordrect, 1979, pp. 53-79.
22. _, Nonlinear scattering at low energy, J. Funct. Anal. 41 (1981), 110-133.
23. R. Strichartz, A priori estimates for the wave equation and some applications, J. Funct. Anal. 5 (1970), 218-235.
24. _, Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J. 44 (1977), 705-714.
25. 3 estimate via incidence geometry, preprint.
26. Y. Zhou, Cauchy problem for semilinear wave equations with small data in four space dimensions, J. Differential Equations 8 (1995), 135-144.