On the lack of compactness and existence of maximizers for some Airy-Strichartz inequalities

This work is devoted to prove a linear profile decomposition for the Airy equation in ${\dot{H}}_x^{s_k}(\mathbb{R})$, where $s_k=(k-4)\mathrm{/}2k$ and $k>4$. We also apply this decomposition to establish the existence of maximizers for a general class of Strichartz type inequalities associated to the Airy equation.