Maximizers for the Strichartz Inequalities for the Wave Equation

Details Maximizers for the Strichartz Inequalities for the Wave Equation Maximizers for the Strichartz Inequalities for the Wave Equation

2009-05-11

arxiv.org/abs/0905.1678v2

Differential and Integral Equations 23 (2010) 1035-1072

Mathematics

Analysis of PDEs

28 pages, revised version, minor changes

Scientific paper

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 $\mathbb{R}^3$.

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