Maximizers for Strichartz Inequalities on the Torus
Analysis of PDEs
2020-02-12 v1
Abstract
We study the existence of maximizers for a one-parameter family of Strichartz inequalities on the torus. In general maximizing sequences can fail to be precompact in , and maximizers can fail to exist. We provide a sufficient condition for precompactness of maximizing sequences (after translation in Fourier space), and verify the existence of maximizers for a range of values of the parameter. Maximizers for the Strichartz inequalities correspond to stable, periodic (in space and time) solutions of a model equation for optical pulses in a dispersion-managed fiber.
Cite
@article{arxiv.2002.04057,
title = {Maximizers for Strichartz Inequalities on the Torus},
author = {Oreoluwa Adekoya and John P. Albert},
journal= {arXiv preprint arXiv:2002.04057},
year = {2020}
}