English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider Benjamin-Bona-Mahony (BBM) equation of the form $$u_t+u_x+uu_x-u_{xxt}=0, \quad (x, t)\in \mathcal{M}\times \mathbb R $$ where$\mathcal{M}= \mathbb T$ or $\mathbb R.$ We establish norm inflation (NI) withinfinite loss of regularity at general initial data in Fourier amalgam andWiener amalgam spaces with negative regularity. This strengthen several knownNI results at zero initial data in $H^s(\mathbb T)$ established by Bona-Dai(2017) and ill-posedness result established by Bona-Tzvetkov (2008) and Panthee(2011) in $H^s(\mathbb R).$ Our result is sharp with respect to localwell-posedness result of Banquet-Villamizar-Roa (2021) in modulation spaces$M^{2,1}_s(\mathbb R)$ for $s\geq 0$.

Norm inflation for BBM equation in Fourier amalgam and Wiener amalgam spaces with negative regularity