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 paper, we consider the well-posedness for the Cauchy problem of theKawahara equation with low regularity data in the periodic case. We obtain thelocal well-posedness for $s \geq -3/2$ by a variant of the Fourier restrictionnorm method. On the other hand, we show the ill-posedness for $s <-3/2$ in weaksense. Moreover, the local solutions can be extended globally in time for $s\geq -1$ by the I-method. This is a shape contrast to the results in thenon-periodic setting, where the critical exponent is equal to -2.

Low regularity data for the periodic Kawahara equation