Local solutions of semilinear wave equations in Hs+1

Mathematical Methods in the Applied Sciences

Volumn 19, Issue 2, 1996, Pages 145-170

  Pecher, Hartmut ^a  

^a UNIVERSITY OF WUPPERTAL   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000530886     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1476(19960125)19:2<145::AID-MMA767>3.0.CO;2-M     Document Type: Article

References (12)

1. Bergh, J. and Löfström, J., Interpolation Spaces, Springer, Berlin, 1976.
2. Brenner, Ph. and von Wahl, W., Global classical solutions to nonlinear wave equations', Math. Z., 176, 87-121 (1981).
3. Cazenave, Th. and Weissler, F. B., "The Cauchy problem for the critical nonlinear Schrödinger equation in H", Nonlinear Analysis, 14, 807-836 (1990).
4. Georgiev, V. and Schirmer, P. P., 'Global existence of low regularity solutions of non-linear wave equations', preprint SFB 256 No. 308 (Bonn, 1993).
5. Ginibre, J. and Velo, G., 'Regularity of solutions of critical and subcritical nonlinear wave equations', preprint LPTHE 92/06 (Orsay, 1992).
6. Kapitanski, L., Weak and yet weaker solutions of semilinear wave equtions, preprint LCDS 93/3 (Providence, 1993).
7. Klainerman, S. and Machedon, M., 'Space-time estimates for null forms and the local existence theorem', Comm. Pure Appl. Math., 46, 1221-1268 (1993).
8. Lindblad, H. and Sogge, C.D., 'On existence and scattering with minimal regularity for semilinear wave equations, J. Functional Analys., to appear.
9. P-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen I, Math. Z., 150, 159-183 (1976).
10. Pecher, H., 'Nonlinear small data scattering for the wave and Klein-Gordon equation', Math. Z., 185, 261-270 (1984).
11. Ponce, G. and Sideris, T.C., 'Local regularity of nonlinear wave equations in three space dimensions', Comm. P.D.E., 18, 169-179 (1993).
12. Triebel, H., Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978.