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

As a continued work of [18], we are concerned with the Timoshenko system inthe case of non-equal wave speeds, which admits the dissipative structure of\textit{regularity-loss}. Firstly, with the modification of a priori estimatesin [18], we construct global solutions to the Timoshenko system pertaining todata in the Besov space with the regularity $s=3/2$. Owing to the weakerdissipative mechanism, extra higher regularity than that for the global-in-timeexistence is usually imposed to obtain the optimal decay rates of classicalsolutions, so it is almost impossible to obtain the optimal decay rates in thecritical space. To overcome the outstanding difficulty, we develop a newfrequency-localization time-decay inequality, which captures the informationrelated to the integrability at the high-frequency part. Furthermore, by theenergy approach in terms of high-frequency and low-frequency decomposition, weshow the optimal decay rate for Timoshenko system in critical Besov spaces,which improves previous works greatly.

Global existence and minimal decay regularity for the Timoshenko system: The case of non-equal wave speeds