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

It is shown that the uniform radius of spatial analyticity $\sigma(t)$ ofsolutions at time $t$ to the KdV equation cannot decay faster than $|t|^{-4/3}$as $|t| \to \infty$ given initial data that is analytic with fixed radius$\sigma_0$. This improves a recent result of Selberg and Da Silva, where theyproved a decay rate of $|t|^{-(4/3 + \varepsilon) }$ for arbitrarily smallpositive $\varepsilon$. The main ingredients in the proof are almostconservation law for the solution to the KdV equation in space of analyticfunctions and space-time dyadic bilinear $L^2$ estimates associated with theKdV equation.

Asymptotic lower bound for the radius of spatial analtyicity to solutions of KdV equation