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

We prove the inviscid limit of the incompressible Navier-Stokes equations inthe same topology of Besov spaces as the initial data. The proof is based onproving the continuous dependence of the Navier-Stokes equations uniformly withrespect to the viscosity. To show the latter, we rely on some Bona-Smith typemethod in the $L^p$ setting. Our obtained result implies a new result that theCauchy problem of the Euler equations is locally well-posed in the borderlineBesov space $B^{\frac dp+1}_{p,1}(\mathbb{R}^d)$, $1\leq p\leq \infty$, $d\geq2$, in the sense of Hadmard, which is an open problem left in recent works byBourgain and Li in \cite{BL,BL1} and by Misio{\l}ek and Yoneda in \cite{MY,MY2,MY3}.

Local well-posedness of the incompressible Euler equations in $B^1_{\infty,1}$ and the inviscid limit of the Navier-Stokes equations