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_1999____A20_0, author = {Klainerman, Sergi\`u and Foschi, Damiano}, title = {On bilinear estimates for wave equations}, journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, year = {1999}, pages = {1-17}, zbl = {01810593}, language = {en}, url = {http://dml.mathdoc.fr/item/JEDP_1999____A20_0} }
Klainerman, Sergiù; Foschi, Damiano. On bilinear estimates for wave equations. Journées équations aux dérivées partielles, (1999), pp. 1-17. http://gdmltest.u-ga.fr/item/JEDP_1999____A20_0/
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