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 editorsBautista, George J.; Potenciano-Machado, Leyter

Journal or seriesJournal of Mathematical Analysis and Applications



Publication year2022

Publication date26/04/2022


Issue number1

Article number126254


Publication countryUnited States

Publication languageEnglish


Publication open accessOpenly available

Publication channel open accessPartially open access channel

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


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.

Keywordspartial differential equationsFourier series

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

Contributing organizations

Ministry reportingYes

Reporting Year2022

JUFO rating1

Last updated on 2024-15-06 at 00:26