TY - JOUR
T1 - Bilinear space-time estimates for homogeneous wave equations
AU - Foschi, Damiano
AU - Klainerman, Sergiu
N1 - Funding Information:
The research of S. Klainerman was partially supported by NSF grant DMS-9400258; supported also by the Pascal Foundation and a Guggenheim fellowship. The authors are grateful to the Laboratoire D’Analyse Numerique of Jussieu and IHES for their kind hospitality. We would like to thank T. Tao for suggesting the Examples 14.7, 14.9, 14.11 and 14.14.
PY - 2000/3
Y1 - 2000/3
N2 - In this paper, we pursue a systematic treatment of the regularity theory for products and bilinear forms of solutions of the homogeneous wave equation. We discuss necessary and sufficient conditions for the validity of bilinear estimates, based on L2 norms in space and time, of derivatives of products of solutions. Also, we give necessary conditions and formulate some conjectures for similar estimates based on LqtLxr norms.
AB - In this paper, we pursue a systematic treatment of the regularity theory for products and bilinear forms of solutions of the homogeneous wave equation. We discuss necessary and sufficient conditions for the validity of bilinear estimates, based on L2 norms in space and time, of derivatives of products of solutions. Also, we give necessary conditions and formulate some conjectures for similar estimates based on LqtLxr norms.
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U2 - 10.1016/S0012-9593(00)00109-9
DO - 10.1016/S0012-9593(00)00109-9
M3 - Article
AN - SCOPUS:0042229265
SN - 0012-9593
VL - 33
SP - 211
EP - 274
JO - Annales Scientifiques de l'Ecole Normale Superieure
JF - Annales Scientifiques de l'Ecole Normale Superieure
IS - 2
ER -