The Benjamin-Ono equation with quasi-periodic data

2025/10/27 by Papenburg, Hagen
#35-xx #35Qxx #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.23599

Abstract

We construct local solutions to the Benjamin-Ono equation for quasi-periodic initial data. The solution is unique among limits of smooth solutions and depends continuously on the data. Our result applies to a richer class of quasi-periodic functions than previous theorems. Central to the argument is an a-priori estimate, the proof of which utilizes Strichartz estimates for quasi-periodic functions obtained recently via decoupling, and a quasi-periodic extension of Tao's gauge transform. As a byproduct of our method, we also establish new local wellposedness results in certain anisotropic Sobolev spaces.

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