Bilinear space-time estimates for homogeneous wave equations

Damiano Foschi; Sergiu Klainerman

doi:10.1016/S0012-9593(00)00109-9

Bilinear space-time estimates for homogeneous wave equations

Damiano Foschi
, Sergiu Klainerman

Mathematics

Research output: Contribution to journal › Article › peer-review

100 Scopus citations

Abstract

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 L^q_tL_x^r norms.

Original language	English (US)
Pages (from-to)	211-274
Number of pages	64
Journal	Annales Scientifiques de l'Ecole Normale Superieure
Volume	33
Issue number	2
DOIs	https://doi.org/10.1016/S0012-9593(00)00109-9
State	Published - Mar 2000

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/S0012-9593(00)00109-9

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title = "Bilinear space-time estimates for homogeneous wave equations",

abstract = "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.",

author = "Damiano Foschi and Sergiu Klainerman",

note = "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{\textquoteright}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.",

year = "2000",

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doi = "10.1016/S0012-9593(00)00109-9",

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journal = "Annales Scientifiques de l'Ecole Normale Superieure",

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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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DO - 10.1016/S0012-9593(00)00109-9

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JO - Annales Scientifiques de l'Ecole Normale Superieure

JF - Annales Scientifiques de l'Ecole Normale Superieure

IS - 2

ER -

Bilinear space-time estimates for homogeneous wave equations

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