Global well-posedness for semi-linear wave equations

Communications in Partial Differential Equations

Volumn 25, Issue 9-10, 2000, Pages 1741-1752

  Kenig, Carlos E ^a   Ponce, Gustavo ^b   Vega, Luis ^c  

^a UNIVERSITY OF CHICAGO   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034353933     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1080/03605300008821565     Document Type: Article

References (10)

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2. Bourgain, J., New global well-posedness results for the nonlinear Schrödinger equations, pre-print.
3. Fonseca, G., Linares, F., and Ponce G., Global well-posedness for the modified Korteweg-de Vries equation, to appear in Comm. P.D.E. 24 (1999), 683-705.
4. 1+1 for rough data, Int. Res. Math. Not. 21 (1998), 1117-1156.
5. Klainerman, S. and Machedon, M., Space-time estimates for null forms and the local existence theorem, Comm. Pure appl. Math. 46 (1993), 1221-1268.
6. Lindblad, H., A sharp counterexample to local existence of low regularity solutions to nonlinear wave equations, Duke Math. J. 72 (1993), 503-539.
7. Lindblad, H. and Sogge, C., On existence and scattering with minimal regularity for semilinear wave equations, J. Funct. Anal. 130 (1995), 357-426.
8. Pecher, H., Nonlinear small data scattering for the wave and Klein-Gordon equations, Math. Z. 185 (1984), 261-270.
9. Staffilani, G., On the growth of high Sobolev norms of solutions for KdV and Schrödinger equations, Duke Math. J. 86 (1997), 109-142.
10. Strichartz, R. S., Restriction of Fourier transforms to quadratic surface and decay of solutions of wave equations, Duke Math. J. 44 (1977), 705-714.