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Preprint
Local well-posedness of the Benjamin-Ono equation with spatially quasiperiodic data
16 Dec 2024
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.
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Details
- Title
- Local well-posedness of the Benjamin-Ono equation with spatially quasiperiodic data
- Creators
- Sultan AitzhanDavid M Ambrose
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991022005187404721