Improved local well-posedness for quasilinear wave equations in dimension three

Duke Mathematical Journal

Volumn 117, Issue 1, 2003, Pages 1-124

  Klainerman, S ^a   Rodnianski, I ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037445111     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-03-11711-1     Document Type: Article

References (16)

1. [BC1] H. BAHOURI and J.-Y. CHEMIN, Équations d'ondes quasilinéaires et effet dispersif, Internat. Math. Res. Notices 1999, 1141-1178. MR 2000i:35125
2. _, Équations d'ondes quasilinéaires et estimation de Strichartz, Amer. J. Math. 121 (1999), 1337-1377. MR 2000i:35124
3. [CK] D. CHRISTODOULOU and S. KLAINERMAN, The Global Nonlinear Stability of the Minkowski Space, Princeton Math. Ser. 41, Princeton Univ. Press, Princeton, 1993. MR 95k:83006
4. [HS] D. HOFFMAN and J. SPRUCK, Sobolev and isoperimetric inequalities for Riemannian submanifolds, Comm. Pure Appl. Math. 27 (1974), 715-727. MR 51:1676
5. [K] L. V. KAPITANSKIǏ, Estimates for norms in Besov and Lizorkin-Triebel spaces for solutions of second-order linear hyperbolic equations, J. Soviet Math. 56 (1991), 2348-2389. MR 90m:35109
6. [K1] S. KLAINERMAN, A commuting vectorfields approach to Strichartz-type inequalities and applications to quasi-linear wave equations, Internat. Math. Res. Notices 2001, 221 -274. MR 2001k:35210
7. [L] H. LINDBLAD, Counterexamples to local existence for semi-linear wave equations, Amer. J. Math. 118 (1996), 1 -16. MR 97b:35124
8. [MSS] 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. MR 93h:58150
9. [PS] G. PONCE and T. SIDERIS, Local regularity of nonlinear wave equations in three space dimensions, Comm. Partial Differential Equations 18 (1993), 169-177. MR 95a:35092
10. [S] L. SIMON, Lectures on Geometric Measure Theory, Proc. Centre Math. Anal. Austral. Nat. Univ. 3, Australian National Univ., Canberra, 1983. MR 87a:49001
11. 1,1 coefficients, Ann. Inst. Fourier (Grenoble) 48 (1998), 797-835. MR 99h:35119
12. [SS] H. F. SMITH and C. D. SOGGE, On Strichartz and eigenfunction estimates for low regularity metrics, Math. Res. Lett. 1 (1994), 729-737. MR 95h:35156
13. [ST] H. F. SMITH and D. TATARU, Sharp counterexamples for Strichartz estimates for low regularity metrics, Math. Res. Lett. 9 (2002), 199-204. CMP 1 909 638
14. [T1] D. TATARU, Strichartz estimates for operators with nonsmooth coefficients and the nonlinear wave equation, Amer. J. Math. 122 (2000), 349-376. MR 2001c:35260
15. [T2] _, Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients, II, Amer. J. Math. 123 (2001), 385-423. MR 2002d:35140
16. [T3] _, Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients, III, J. Amer. Math. Soc. 15 (2002), 419-442. MR 2003a:35120