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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We construct an example showing that the solution map of the Euler equationsis not continuous in the H\"older space from $C^{1,\alpha}$ to$L^\infty_tC^{1,\alpha}_x$ for any $0<\alpha<1$. On the other hand we show thatit is continuous when restricted to the little H\"older subspace$c^{1,\alpha}$. We apply the latter to prove an ill-posedness result forsolutions of the vorticity equations in Besov spaces near the critical space$B^1_{2,1}$. As a consequence we show that a sequence of best constants of theSobolev embedding theorem near the critical function space is not continuous.

Continuity of the solution map of the Euler equations in H\"older spaces and weak norm inflation in Besov spaces