Maximizers for the Strichartz Inequalities for the wave equation

Abstract

We prove the existence of maximizers for Strichartz inequalities for the wave equation in dimensions $d\geq 3$. Our approach follows the scheme given by Shao in [21] which obtains the existence of maximizers in the context of the Schrödinger equation. The main tool that we use is the linear profile decomposition for the wave equation which we prove in $\mathbb{R}^d$, $d\geq 3$, extending the profile decomposition result of Bahouri and Gerard [1], previously obtained in $\mathbb{R}^3$.