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 theory, which is now quite well developed, I plan to discuss a more general point of view concerning the 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.
@article{JEDP_1998____A7_0,
author = {Klainerman, Sergi\`u},
title = {On bilinear restriction type estimates and applications to nonlinear wave equations},
journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
year = {1998},
pages = {1-1},
language = {en},
url = {http://dml.mathdoc.fr/item/JEDP_1998____A7_0}
}
Klainerman, Sergiù. On bilinear restriction type estimates and applications to nonlinear wave equations. Journées équations aux dérivées partielles, (1998), p. 1. http://gdmltest.u-ga.fr/item/JEDP_1998____A7_0/