  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, which obtains the existence of maximizers in the context of the
Schr\"odinger 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,
previously obtained in $\mathbb{R}^3$.
