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

In this note, we prove the local well-posedness in the energy space of the$k$-generalized Zakharov-Kuznetsov equation posed on $ \R\times \T $ for anypower non-linearity $ k\ge 2$. Moreover, we obtain global solutions under aprecise smallness assumption on the initial data by proving a sharp GagliardoNirenberg type inequality.

A note on the well-posedness in the energy space for the generalized ZK equation posed on $\mathbb{R}\times\mathbb{T}$