Norm-inflation results for purely BBM-type Boussinesq systems
Abstract
This article is concerned with the norm-inflation phenomena associated with a periodic initial-value abcd-Benjamin-Bona-Mahony type Boussinesq system. We show that the initial-value problem is ill-posed in the periodic Sobolev spaces H−sp (0, 2π)×H−sp (0, 2π) for all s > 0. Our proof is constructive, in the sense that we provide smooth initial data that generates solutions arbitrarily large in H−sp (0, 2π) × H−sp (0, 2π)-norm for arbitrarily short time. This result is sharp since in [15] the well-posedness is proved to holding for all positive periodic Sobolev indexes of the form Hsp (0, 2π) × Hsp (0, 2π), including s = 0.
Main Authors
Format
Articles
Research article
Published
2022
Series
Subjects
Publication in research information system
Publisher
Elsevier
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202205042540Use this for linking
Review status
Peer reviewed
ISSN
0022-247X
DOI
https://doi.org/10.1016/j.jmaa.2022.126254
Language
English
Published in
Journal of Mathematical Analysis and Applications
Citation
- Bautista, G. J., & Potenciano-Machado, L. (2022). Norm-inflation results for purely BBM-type Boussinesq systems. Journal of Mathematical Analysis and Applications, 514(1), Article 126254. https://doi.org/10.1016/j.jmaa.2022.126254
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Additional information about funding
G. J. B was partially supported by the Universidad Privada del Norte, Lima-Perú. L. P-M thanks the Department of Mathematics and Statistics of the University of Jyväskylä, Finland, for providing an excellent environment to prepare this manuscript.
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