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/

Zendy Plus

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

Zendy Tools

Zendy Open

In this paper, we consider the Cauchy problem for a class of weaklydissipative Camassa-Holm equations in nonhomogeneous Besov spaces. First, weprove that the Cauchy problem admits a unique global strong solution in Besovspaces with proper condition on the dissipation parameter $\lambda>0$. Thenovel ingredients in the proof lies in transforming the equations into a classof damped Camassa-Holm equations, and performing a non-standard iterativemethod. It is shown that our result holds for the damped equations with moregeneral time-dependent parameters, which improves the existed results fromSobolev spaces to Besov spaces without assuming any sign condition on theinitial data. Second, we derive two kinds of blow-up criteria in suitableSobolev spaces, which in some sense inform us how the dissipation parameter$\lambda$ influences the singularity formation of strong solutions.

New results on the global solvability and blow-up for a class of weakly dissipative Camassa-Holm equations