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

This work is a series of two articles. The main goal is to rigorously derivethe degenerate parabolic-elliptic Keller-Segel system in the sub-criticalregime from a moderately interacting stochastic particle system. In the firstarticle [7], we establish the classical solution theory of the degenerateparabolic-elliptic Keller-Segel system and its non-local version. In the secondarticle, which is the current one, we derive a propagation of chaos result,where the classical solution theory obtained in the first article is used toderive required estimates for the particle system. Due to the degeneracy of thenon-linear diffusion and the singular aggregation effect in the system, weperform an approximation of the stochastic particle system by using a cut-offedinteracting potential. An additional linear diffusion on the particle level isused as a parabolic regularization of the system. We present the propagation ofchaos result with logarithmic scalings. Consequently, the propagation of chaosfollows directly from convergence in the sense of expectation and the vanishingviscosity argument of the Keller-Segel system.

Rigorous Derivation of the Degenerate Parabolic-Elliptic Keller-Segel  System from a Moderately Interacting Stochastic Particle System. Part II  Propagation of Chaos