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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider the Euler alignment system with mildly singular interactionkernels. When the local repulsion term is of the fractional type, global intime existence of smooth solutions was provedin\cite{do2018global,shvydkoy2017eulerian1,shvydkoy2017eulerian2,shvydkoy2017eulerian3}.Here, we consider a class of less singular interaction kernels and establishthe global regularity of solutions as long as the interaction kernels are notintegrable. The proof relies on modulus of continuity estimates for a class ofparabolic integro-differential equations with a drift and mildly singularkernels.

Global well-posedness for the Euler alignment system with mildly singular interactions