Bilinear space-time estimates for homogeneous wave equations

Authors
Foschi, D Klainerman, S
Citation
D. Foschi et S. Klainerman, Bilinear space-time estimates for homogeneous wave equations, ANN SCI EC, 33(2), 2000, pp. 211-274
Citations number
24
Categorie Soggetti
Mathematics
Journal title
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE
ISSN journal
00129593 → ACNP
Volume
33
Issue
2
Year of publication
2000
Pages
211 - 274
Database
ISI
SICI code
0012-9593(200003/04)33:2<211:BSEFHW>2.0.ZU;2-9
Abstract
In this paper, we pursue a systematic treatment of the regularity theory fo r products and bilinear forms of solutions of the homogeneous wave equation . We discuss necessary and sufficient conditions for the validity of biline ar estimates, based on L-2 norms in space and time, of derivatives of produ cts of solutions. Also, we give necessary conditions and formulate some con jectures for similar estimates based on (LtLxr)-L-q, norms. (C) 2000 Editio ns scientifiques et medicales Elsevier SAS.