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

We prove uniform H\"older regularity estimates for a transport-diffusionequation with a fractional diffusion operator,and a general advection field inBMO, as long as the order of the diffusion dominates the transport term atsmall scales;our only requirement is the smallness of the negative part of thedivergence in some critical Lebesgue space. In comparison to a celebratedresult by L.Silvestre (2012), our advection field does not need to be bounded.A similar result can be obtained in the super-critical case if the advectionfield is H\"older continuous. Our proof is inspired by A.Kiselev and F.Nazarov(2010) and is based on the dual evolution technique. The idea is to propagatean atom property (i.e. localization and integrability in Lebesgue spaces) underthe dual conservation law, when it is coupled with the fractional diffusionoperator.

Variation on a theme by Kiselev and Nazarov: H{\"o}lder estimates for non-local transport-diffusion, along a non-divergence-free BMO field