Prelectura de tesis

Doctorando: Giuseppe Negro (UAM-ICMAT & Université Paris 13).

Directores de tesis: Keith Rogers (ICMAT), Thomas Duyckaerts (UP13).

Título: Sharp estimates for linear and nonlinear wave equations via the Penrose
transform.

Jueves 13 de diciembre

15:30 hr, Módulo 17, aula 520

Resumen: In 2006, Damiano Foschi found the sharp constant in the Strichartz estimate for the wave equation in $R^{3+1}$ and conjectured what the maximizers should be in other dimensions. On the one hand, we will see how his inequality can be sharpened further, adding a term which is zero on the maximizers, and on the other hand we will disprove his conjecture in even dimensions. For this we will take advantage of a conformal transformation which compactifies the  space-time.  We will also present a sharp estimate for the scattering norm of the cubic wave equation on Minkowski space with data in the critical $L^{^2}$-Sobolev space.