Maximizers for Strichartz Inequalities on the Torus

2020/02/10 by Adekoya, Oreoluwa, Albert, John P.
#35Q55 (Primary) 35B45 (Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.04057

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 L²(\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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