Local well-posedness of the Benjamin-Ono equation with spatially quasiperiodic data
Analysis of PDEs
2024-12-18 v1
Abstract
We consider the Benjamin-Ono equation in the spatially quasiperiodic setting. We establish local well-posedness of the initial value problem with initial data in quasiperiodic Sobolev spaces. This requires developing some of the fundamental properties of Sobolev spaces and the energy method for quasiperiodic functions. We discuss prospects for global existence. We demonstrate that while conservation laws still hold, these quantities no longer control the associated Sobolev norms, thereby preventing the establishment of global results by usual arguments.
Keywords
Cite
@article{arxiv.2412.12457,
title = {Local well-posedness of the Benjamin-Ono equation with spatially quasiperiodic data},
author = {Sultan Aitzhan and David M. Ambrose},
journal= {arXiv preprint arXiv:2412.12457},
year = {2024}
}