## Differential and Integral Equations

### Maximizers for the Strichartz Inequalities for the wave equation

Aynur Bulut

#### 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 $\mathbb{R}^3$.

#### Article information

Source
Differential Integral Equations, Volume 23, Number 11/12 (2010), 1035-1072.

Dates
First available in Project Euclid: 20 December 2012

https://projecteuclid.org/euclid.die/1356019072

Mathematical Reviews number (MathSciNet)
MR2742477

Zentralblatt MATH identifier
1240.35314

Subjects
Primary: 35L05: Wave equation

#### Citation

Bulut, Aynur. Maximizers for the Strichartz Inequalities for the wave equation. Differential Integral Equations 23 (2010), no. 11/12, 1035--1072. https://projecteuclid.org/euclid.die/1356019072