BILINEAR ESTIMATES ON CURVED SPACE-TIMES

Sergiu Klainerman; Igor Rodnianski

doi:10.1142/S0219891605000440

BILINEAR ESTIMATES ON CURVED SPACE-TIMES

Sergiu Klainerman, Igor Rodnianski

Mathematics

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

13 Scopus citations

Abstract

To settle the L² bounded curvature conjecture for the Einstein-vaccum equations one needs to prove bilinear type estimates for solutions of the homogeneous wave equation on a fixed background with H² local regularity. In this paper we introduce a notion of primitive parametrix for the homogeneous wave equation for which we can prove, under very broad assumptions, the desired bilinear estimates.

Original language	English (US)
Pages (from-to)	279-291
Number of pages	13
Journal	Journal of Hyperbolic Differential Equations
Volume	2
Issue number	2
DOIs	https://doi.org/10.1142/S0219891605000440
State	Published - Jun 1 2005

All Science Journal Classification (ASJC) codes

Analysis
General Mathematics

Keywords

Bilinear
curved
wave equation

Access to Document

10.1142/S0219891605000440

Cite this

@article{9ae1d97d7b114712b07361d070c932ff,

title = "BILINEAR ESTIMATES ON CURVED SPACE-TIMES",

abstract = "To settle the L2 bounded curvature conjecture for the Einstein-vaccum equations one needs to prove bilinear type estimates for solutions of the homogeneous wave equation on a fixed background with H2 local regularity. In this paper we introduce a notion of primitive parametrix for the homogeneous wave equation for which we can prove, under very broad assumptions, the desired bilinear estimates.",

keywords = "Bilinear, curved, wave equation",

author = "Sergiu Klainerman and Igor Rodnianski",

note = "Publisher Copyright: {\textcopyright} 2005 World Scientific Publishing Company.",

year = "2005",

month = jun,

day = "1",

doi = "10.1142/S0219891605000440",

language = "English (US)",

volume = "2",

pages = "279--291",

journal = "Journal of Hyperbolic Differential Equations",

issn = "0219-8916",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "2",

}

TY - JOUR

T1 - BILINEAR ESTIMATES ON CURVED SPACE-TIMES

AU - Klainerman, Sergiu

AU - Rodnianski, Igor

PY - 2005/6/1

Y1 - 2005/6/1

N2 - To settle the L2 bounded curvature conjecture for the Einstein-vaccum equations one needs to prove bilinear type estimates for solutions of the homogeneous wave equation on a fixed background with H2 local regularity. In this paper we introduce a notion of primitive parametrix for the homogeneous wave equation for which we can prove, under very broad assumptions, the desired bilinear estimates.

AB - To settle the L2 bounded curvature conjecture for the Einstein-vaccum equations one needs to prove bilinear type estimates for solutions of the homogeneous wave equation on a fixed background with H2 local regularity. In this paper we introduce a notion of primitive parametrix for the homogeneous wave equation for which we can prove, under very broad assumptions, the desired bilinear estimates.

KW - Bilinear

KW - curved

KW - wave equation

UR - http://www.scopus.com/inward/record.url?scp=58249094595&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=58249094595&partnerID=8YFLogxK

U2 - 10.1142/S0219891605000440

DO - 10.1142/S0219891605000440

M3 - Article

AN - SCOPUS:58249094595

SN - 0219-8916

VL - 2

SP - 279

EP - 291

JO - Journal of Hyperbolic Differential Equations

JF - Journal of Hyperbolic Differential Equations

IS - 2

ER -

BILINEAR ESTIMATES ON CURVED SPACE-TIMES

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this