A1 Journal article (refereed)
Norm-inflation results for purely BBM-type Boussinesq systems (2022)

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

JYU authors or editors

Publication details

All authors or editors: Bautista, George J.; Potenciano-Machado, Leyter

Journal or series: Journal of Mathematical Analysis and Applications

ISSN: 0022-247X

eISSN: 1096-0813

Publication year: 2022

Publication date: 26/04/2022

Volume: 514

Issue number: 1

Article number: 126254

Publisher: Elsevier

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1016/j.jmaa.2022.126254

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/80878

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.

Keywords: partial differential equations; Fourier series

Free keywords: Boussinesq system; Benjamin-Bona Mahony equation; spectral analysis; Fourier series; norm inflation; Picard's iteration; Duhamel's principle

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2022

Preliminary JUFO rating: 1