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arXiv · 2002.04057

Maximizers for Strichartz Inequalities on the Torus

Oreoluwa Adekoya·John P. Albert
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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 $L^2(\mathbb T)$, 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.

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Oreoluwa Adekoya, John P. Albert. 2020-02-10. Maximizers for Strichartz Inequalities on the Torus. https://arxiv.org/abs/2002.04057

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