On bilinear restriction type estimates and applications to nonlinear wave equations

Klainerman, Sergiù. "On bilinear restriction type estimates and applications to nonlinear wave equations." Journées équations aux dérivées partielles (1998): 1-1. <http://eudml.org/doc/93364>.

@article{Klainerman1998,
abstract = {I will start with a short review of the classical restriction theorem for the sphere and Strichartz estimates for the wave equation. I then plan to give a detailed presentation of their recent generalizations in the form of “bilinear estimates”. In addition to the $L^2$ theory, which is now quite well developed, I plan to discuss a more general point of view concerning the $L^p$ theory. By investigating simple examples I will derive necessary conditions for such estimates to be true. I also plan to discuss the relevance of these estimates to nonlinear wave equations.},
author = {Klainerman, Sergiù},
journal = {Journées équations aux dérivées partielles},
keywords = {optimal well posedness; Yang-Mills equations in the Lorentz gauge; Wave-Maps equations; Strichartz-Pecher inequalities},
language = {eng},
pages = {1-1},
publisher = {Université de Nantes},
title = {On bilinear restriction type estimates and applications to nonlinear wave equations},
url = {http://eudml.org/doc/93364},
year = {1998},
}

TY - JOUR
AU - Klainerman, Sergiù
TI - On bilinear restriction type estimates and applications to nonlinear wave equations
JO - Journées équations aux dérivées partielles
PY - 1998
PB - Université de Nantes
SP - 1
EP - 1
AB - I will start with a short review of the classical restriction theorem for the sphere and Strichartz estimates for the wave equation. I then plan to give a detailed presentation of their recent generalizations in the form of “bilinear estimates”. In addition to the $L^2$ theory, which is now quite well developed, I plan to discuss a more general point of view concerning the $L^p$ theory. By investigating simple examples I will derive necessary conditions for such estimates to be true. I also plan to discuss the relevance of these estimates to nonlinear wave equations.
LA - eng
KW - optimal well posedness; Yang-Mills equations in the Lorentz gauge; Wave-Maps equations; Strichartz-Pecher inequalities
UR - http://eudml.org/doc/93364
ER -