On bilinear restriction type estimates and applications to nonlinear wave equations

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.

Locations

• Journées Équations aux dérivées partielles - View - PDF
• French digital mathematics library (Numdam) - View - PDF