Nonlinear phenomena in dispersive equations

A sharpened Strichartz inequality for the wave equation

23 mai 2018, 16:40

50m

Salle de Réunion - Bâtiment M2 (Laboratoire Paul Painlevé)

Orateur

Giuseppe Negro

Description

In 2004, Foschi found the best constant, and the extremizing functions, for the Strichartz inequality for the wave equation with data in the Sobolev space ${\dot{H}}^{1/2}\times {\dot{H}}^{-1/2}({\mathbf{R}}^3)$. We refine this inequality, by adding a term proportional to the distance of the initial data from the set of extremizers. Foschi also formulated a conjecture, concerning the extremizers to this Strichartz inequality in all spatial dimensions $d\ge 2$. We disprove such conjecture for even $d$, but we provide evidence to support it for odd $d$. The proofs use the conformal compactification of the Minkowski space-time given by the Penrose transform.