Regularity and geometric properties of solutions of the Einstein-Vacuum equations

Sergiu Klainerman; Igor Rodnianski

Journées équations aux dérivées partielles (2002)

  • Volume: 334, Issue: 2, page 1-14
  • ISSN: 0752-0360

Abstract

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We review recent results concerning the study of rough solutions to the initial value problem for the Einstein vacuum equations expressed relative to wave coordinates. We develop new analytic methods based on Strichartz type inequalities which results in a gain of half a derivative relative to the classical result. Our methods blend paradifferential techniques with a geometric approach to the derivation of decay estimates. The latter allows us to take full advantage of the specific structure of the Einstein equations.

How to cite

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Klainerman, Sergiu, and Rodnianski, Igor. "Regularity and geometric properties of solutions of the Einstein-Vacuum equations." Journées équations aux dérivées partielles 334.2 (2002): 1-14. <http://eudml.org/doc/93426>.

@article{Klainerman2002,
abstract = {We review recent results concerning the study of rough solutions to the initial value problem for the Einstein vacuum equations expressed relative to wave coordinates. We develop new analytic methods based on Strichartz type inequalities which results in a gain of half a derivative relative to the classical result. Our methods blend paradifferential techniques with a geometric approach to the derivation of decay estimates. The latter allows us to take full advantage of the specific structure of the Einstein equations.},
author = {Klainerman, Sergiu, Rodnianski, Igor},
journal = {Journées équations aux dérivées partielles},
keywords = {paradifferential techniques; Strichartz-type inequalities},
language = {eng},
number = {2},
pages = {1-14},
publisher = {Université de Nantes},
title = {Regularity and geometric properties of solutions of the Einstein-Vacuum equations},
url = {http://eudml.org/doc/93426},
volume = {334},
year = {2002},
}

TY - JOUR
AU - Klainerman, Sergiu
AU - Rodnianski, Igor
TI - Regularity and geometric properties of solutions of the Einstein-Vacuum equations
JO - Journées équations aux dérivées partielles
PY - 2002
PB - Université de Nantes
VL - 334
IS - 2
SP - 1
EP - 14
AB - We review recent results concerning the study of rough solutions to the initial value problem for the Einstein vacuum equations expressed relative to wave coordinates. We develop new analytic methods based on Strichartz type inequalities which results in a gain of half a derivative relative to the classical result. Our methods blend paradifferential techniques with a geometric approach to the derivation of decay estimates. The latter allows us to take full advantage of the specific structure of the Einstein equations.
LA - eng
KW - paradifferential techniques; Strichartz-type inequalities
UR - http://eudml.org/doc/93426
ER -

References

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